394
Views
102
CrossRef citations to date
0
Altmetric
Original Articles

An efficient method for recovering Lyapunov vectors from singular vectors

&
Pages 355-366 | Received 24 May 2006, Accepted 02 Feb 2007, Published online: 15 Dec 2016

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (5)

Marc Bocquet & Alberto Carrassi. (2017) Four-dimensional ensemble variational data assimilation and the unstable subspace. Tellus A: Dynamic Meteorology and Oceanography 69:1.
Read now
Gary Morriss & Daniel Truant. (2011) Finite-size scaling of Lyapunov spectra for quasi-one-dimensional hard discs. Molecular Simulation 37:4, pages 277-283.
Read now
S. Herrera, D. Paz ó, J. Ferná Ndez & M. A. RodríGuez. (2011) The role of large-scale spatial patterns in the chaotic amplification of perturbations in a Lorenz’96 model. Tellus A: Dynamic Meteorology and Oceanography 63:5, pages 978-990.
Read now
Gene-Hua Crystalng, Dennis Mclaughlin, Dara Entekhabi & Adel Ahanin. (2011) The role of model dynamics in ensemble Kalman filter performance for chaotic systems. Tellus A: Dynamic Meteorology and Oceanography 63:5, pages 958-977.
Read now
Diego Pazó, Miguel A. Rodríguez & Juan M. López,. (2010) Spatio-temporal evolution of perturbations in ensembles initialized by bred, Lyapunov and singular vectors. Tellus A: Dynamic Meteorology and Oceanography 62:1, pages 10-23.
Read now

Articles from other publishers (97)

J. Barbish & M. R. Paul. (2023) Using covariant Lyapunov vectors to quantify high-dimensional chaos with a conservation law. Physical Review E 108:5.
Crossref
Jorgen S. Frederiksen. (2023) Covariant Lyapunov Vectors and Finite-Time Normal Modes for Geophysical Fluid Dynamical Systems. Entropy 25:2, pages 244.
Crossref
Swetamber Das & Jason R. Green. (2022) Density matrix formulation of dynamical systems. Physical Review E 106:5.
Crossref
Akim Viennet, Nikki Vercauteren, Maximilian Engel & Davide Faranda. (2022) Guidelines for data-driven approaches to study transitions in multiscale systems: The case of Lyapunov vectors. Chaos: An Interdisciplinary Journal of Nonlinear Science 32:11.
Crossref
E. L. Brugnago, C. C. Felicio & M. W. Beims. (2022) Forecasting the Duration of Three Connected Wings in a Generalized Lorenz Model. International Journal of Bifurcation and Chaos 32:13.
Crossref
Miguel A. Prado Reynoso & Marcus W. Beims. (2022) Studying finite-time (non)-domination in dynamical systems using Oseledec’s splitting. Application to the standard map. Communications in Nonlinear Science and Numerical Simulation 110, pages 106358.
Crossref
Christoph Martin, Nahal Sharafi & Sarah Hallerberg. (2022) Estimating covariant Lyapunov vectors from data. Chaos: An Interdisciplinary Journal of Nonlinear Science 32:3.
Crossref
Courtney Quinn, Terence J. O’Kane & Dylan Harries. (2022) Systematic calculation of finite-time mixed singular vectors and characterization of error growth for persistent coherent atmospheric disturbances over Eurasia. Chaos: An Interdisciplinary Journal of Nonlinear Science 32:2.
Crossref
Yumeng Chen, Alberto Carrassi & Valerio Lucarini. (2021) Inferring the instability of a dynamical system from the skill of data assimilation exercises. Nonlinear Processes in Geophysics 28:4, pages 633-649.
Crossref
Sergey Gonchenko, Alexey Kazakov & Dmitry Turaev. (2021) Wild pseudohyperbolic attractor in a four-dimensional Lorenz system. Nonlinearity 34:4, pages 2018-2047.
Crossref
Miguel A. Prado Reynoso, Rafael M. da Silva & Marcus W. Beims. (2021) Studying partial hyperbolicity inside regimes of motion in Hamiltonian systems. Chaos, Solitons & Fractals 144, pages 110640.
Crossref
Florian Noethen. (2021) Computing Covariant Lyapunov Vectors in Hilbert spaces. Journal of Computational Dynamics 8:3, pages 325.
Crossref
D. Lasagna. (2020) Sensitivity of long periodic orbits of chaotic systems. Physical Review E 102:5.
Crossref
Pavel V. Kuptsov & Sergey P. Kuznetsov. (2020) Route to hyperbolic hyperchaos in a nonautonomous time-delay system. Chaos: An Interdisciplinary Journal of Nonlinear Science 30:11, pages 113113.
Crossref
Eduardo L. Brugnago, Jason A. C. Gallas & Marcus W. Beims. (2020) Predicting regime changes and durations in Lorenz’s atmospheric convection model. Chaos: An Interdisciplinary Journal of Nonlinear Science 30:10.
Crossref
Ryne Beeson & N. Sri Namachchivaya. (2020) Particle filtering for chaotic dynamical systems using future right-singular vectors. Nonlinear Dynamics 102:2, pages 679-696.
Crossref
Eduardo L. Brugnago, Jason A. C. Gallas & Marcus W. Beims. (2020) Machine learning, alignment of covariant Lyapunov vectors, and predictability in Rikitake’s geomagnetic dynamo model. Chaos: An Interdisciplinary Journal of Nonlinear Science 30:8.
Crossref
Maxime Tondeur, Alberto Carrassi, Stephane Vannitsem & Marc Bocquet. (2020) On Temporal Scale Separation in Coupled Data Assimilation with the Ensemble Kalman Filter. Journal of Statistical Physics 179:5-6, pages 1161-1185.
Crossref
Courtney Quinn, Terence J. O'Kane & Vassili Kitsios. (2020) Application of a local attractor dimension to reduced space strongly coupled data assimilation for chaotic multiscale systems. Nonlinear Processes in Geophysics 27:1, pages 51-74.
Crossref
Valerio Lucarini & Andrey Gritsun. (2019) A new mathematical framework for atmospheric blocking events. Climate Dynamics 54:1-2, pages 575-598.
Crossref
Karim Shawki & George Papadakis. (2019) A preconditioned Multiple Shooting Shadowing algorithm for the sensitivity analysis of chaotic systems. Journal of Computational Physics 398, pages 108861.
Crossref
Antoine Blanchard & Themistoklis P. Sapsis. (2019) Learning the tangent space of dynamical instabilities from data. Chaos: An Interdisciplinary Journal of Nonlinear Science 29:11.
Crossref
Florian Noethen. (2019) A projector-based convergence proof of the Ginelli algorithm for covariant Lyapunov vectors. Physica D: Nonlinear Phenomena 396, pages 18-34.
Crossref
Kevin Höhlein, Felix P. Kemeth & Katharina Krischer. (2019) Lyapunov spectra and collective modes of chimera states in globally coupled Stuart-Landau oscillators. Physical Review E 100:2.
Crossref
Pavel V. Kuptsov & Anna V. Kuptsova. (2018) Estimating of the inertial manifold dimension for a chaotic attractor of complex Ginzburg-Landau equation using a neural network. Estimating of the inertial manifold dimension for a chaotic attractor of complex Ginzburg-Landau equation using a neural network.
Malik Hassanaly & Venkat Raman. (2019) Numerical convergence of the Lyapunov spectrum computed using low Mach number solvers. Journal of Computational Physics 386, pages 467-485.
Crossref
R. Levanger, M. Xu, J. Cyranka, M. F. Schatz, K. Mischaikow & M. R. Paul. (2019) Correlations between the leading Lyapunov vector and pattern defects for chaotic Rayleigh-Bénard convection. Chaos: An Interdisciplinary Journal of Nonlinear Science 29:5.
Crossref
Malik Hassanaly & Venkat Raman. (2019) Ensemble-LES analysis of perturbation response of turbulent partially-premixed flames. Proceedings of the Combustion Institute 37:2, pages 2249-2257.
Crossref
Juan C. Vallejo & Miguel A. F. SanjuanJuan C. Vallejo & Miguel A. F. Sanjuan. 2019. Predictability of Chaotic Dynamics. Predictability of Chaotic Dynamics 33 69 .
Brent Giggins & Georg A. Gottwald. (2019) Stochastically perturbed bred vectors in multi‐scale systems. Quarterly Journal of the Royal Meteorological Society 145:719, pages 642-658.
Crossref
Pavel V. Kuptsov & Sergey P. Kuznetsov. (2019) Lyapunov Analysis of Strange Pseudohyperbolic Attractors: Angles Between Tangent Subspaces, Local Volume Expansion and Contraction. Regular and Chaotic Dynamics 23:7-8, pages 908-932.
Crossref
Lesley De Cruz, Sebastian Schubert, Jonathan Demaeyer, Valerio Lucarini & Stéphane Vannitsem. (2018) Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models. Nonlinear Processes in Geophysics 25:2, pages 387-412.
Crossref
M-A. Nikolaidis, B. F. Farrell & P. J. Ioannou. (2018) The mechanism by which nonlinearity sustains turbulence in plane Couette flow. Journal of Physics: Conference Series 1001, pages 012014.
Crossref
M. Xu & M. R. Paul. (2018) Spatiotemporal dynamics of the covariant Lyapunov vectors of chaotic convection. Physical Review E 97:3.
Crossref
Pavel V. Kuptsov & Sergey P. Kuznetsov. (2018) Numerical test for hyperbolicity in chaotic systems with multiple time delays. Communications in Nonlinear Science and Numerical Simulation 56, pages 227-239.
Crossref
Marcus W. Beims & Jason A. C. Gallas. (2018) Predictability of the onset of spiking and bursting in complex chemical reactions. Physical Chemistry Chemical Physics 20:27, pages 18539-18546.
Crossref
Giovanni Conti & Gualtiero Badin. (2017) Hyperbolic Covariant Coherent Structures in Two Dimensional Flows. Fluids 2:4, pages 50.
Crossref
Nahal Sharafi, Marc Timme & Sarah Hallerberg. (2017) Critical transitions and perturbation growth directions. Physical Review E 96:3.
Crossref
Brian F. Farrell & Petros J. Ioannou. (2017) Statistical state dynamics-based analysis of the physical mechanisms sustaining and regulating turbulence in Couette flow. Physical Review Fluids 2:8.
Crossref
Antonio Politi, Arkady Pikovsky & Ekkehard Ullner. (2017) Chaotic macroscopic phases in one-dimensional oscillators. The European Physical Journal Special Topics 226:9, pages 1791-1810.
Crossref
Andrey Gritsun & Valerio Lucarini. (2017) Fluctuations, response, and resonances in a simple atmospheric model. Physica D: Nonlinear Phenomena 349, pages 62-76.
Crossref
Valerio Lucarini, Francesco Ragone & Frank Lunkeit. (2016) Predicting Climate Change Using Response Theory: Global Averages and Spatial Patterns. Journal of Statistical Physics 166:3-4, pages 1036-1064.
Crossref
Marc Bocquet, Karthik S. Gurumoorthy, Amit Apte, Alberto Carrassi, Colin Grudzien & Christopher K. R. T. Jones. (2017) Degenerate Kalman Filter Error Covariances and Their Convergence onto the Unstable Subspace. SIAM/ASA Journal on Uncertainty Quantification 5:1, pages 304-333.
Crossref
Marcus W. Beims & Jason A. C. Gallas. (2016) Alignment of Lyapunov Vectors: A Quantitative Criterion to Predict Catastrophes?. Scientific Reports 6:1.
Crossref
C.A. Jousseph, T.S. Kruger, C. Manchein, S.R. Lopes & M.W. Beims. (2016) Weak dissipative effects on trajectories from the edge of basins of attraction. Physica A: Statistical Mechanics and its Applications 456, pages 68-74.
Crossref
X. Ding, H. Chaté, P. Cvitanović, E. Siminos & K. A. Takeuchi. (2016) Estimating the Dimension of an Inertial Manifold from Unstable Periodic Orbits. Physical Review Letters 117:2.
Crossref
Pavel V. Kuptsov & Sergey P. Kuznetsov. (2016) Numerical test for hyperbolicity of chaotic dynamics in time-delay systems. Physical Review E 94:1.
Crossref
K.D. Mease, U. Topcu, E. Aykutluğ & M. Maggia. (2016) Characterizing two-timescale nonlinear dynamics using finite-time Lyapunov exponents and subspaces. Communications in Nonlinear Science and Numerical Simulation 36, pages 148-174.
Crossref
Erkut Aykutlug, Ufuk Topcu & Kenneth D. Mease. (2016) Manifold-Following Approximate Solution of Completely Hypersensitive Optimal Control Problems. Journal of Optimization Theory and Applications 170:1, pages 220-242.
Crossref
Sebastian Schubert & Valerio Lucarini. (2016) Dynamical analysis of blocking events: spatial and temporal fluctuations of covariant Lyapunov vectors. Quarterly Journal of the Royal Meteorological Society 142:698, pages 2143-2158.
Crossref
Stéphane Vannitsem & Valerio Lucarini. (2016) Statistical and dynamical properties of covariant lyapunov vectors in a coupled atmosphere-ocean model—multiscale effects, geometric degeneracy, and error dynamics. Journal of Physics A: Mathematical and Theoretical 49:22, pages 224001.
Crossref
M. Xu & M. R. Paul. (2016) Covariant Lyapunov vectors of chaotic Rayleigh-Bénard convection. Physical Review E 93:6.
Crossref
Marcus W. Beims & Jason A. C. Gallas. (2016) Manifold angles, the concept of self-similarity and angle-enhanced bifurcation diagrams. Scientific Reports 6:1.
Crossref
Henk Dijkstra. (2016) A Normal Mode Perspective of Intrinsic Ocean-Climate Variability. Annual Review of Fluid Mechanics 48:1, pages 341-363.
Crossref
Xiong Ding & Predrag Cvitanović. (2016) Periodic Eigendecomposition and Its Application to Kuramoto--Sivashinsky System. SIAM Journal on Applied Dynamical Systems 15:3, pages 1434-1454.
Crossref
Ying Zhang, Kayo Ide & Eugenia Kalnay. (2015) Bred vectors of the Lorenz63 system. Advances in Atmospheric Sciences 32:11, pages 1533-1538.
Crossref
Sebastian Schubert & Valerio Lucarini. (2015) Covariant Lyapunov vectors of a quasi‐geostrophic baroclinic model: analysis of instabilities and feedbacks. Quarterly Journal of the Royal Meteorological Society 141:693, pages 3040-3055.
Crossref
Pierre Gaspard. (2015) Cycles, randomness, and transport from chaotic dynamics to stochastic processes. Chaos: An Interdisciplinary Journal of Nonlinear Science 25:9.
Crossref
M. Sala & R. Artuso. (2015) Oseledets' splitting of standard-like maps. Chaos: An Interdisciplinary Journal of Nonlinear Science 25:2, pages 023113.
Crossref
F. Uboldi & A. Trevisan. (2015) Multiple-scale error growth in a convection-resolving model. Nonlinear Processes in Geophysics 22:1, pages 1-13.
Crossref
Philip BittihnPhilip Bittihn. 2015. Complex Structure and Dynamics of the Heart. Complex Structure and Dynamics of the Heart 25 84 .
Daniel P. Truant & Gary P. Morriss. (2014) Backward and covariant Lyapunov vectors and exponents for hard-disk systems with a steady heat current. Physical Review E 90:5.
Crossref
Hadrien Bosetti & Harald A. Posch. (2014) What Does Dynamical Systems Theory Teach Us about Fluids?. Communications in Theoretical Physics 62:4, pages 451-468.
Crossref
Pavel V. Kuptsov & Anna V. Kuptsova. (2014) Predictable nonwandering localization of covariant Lyapunov vectors and cluster synchronization in scale-free networks of chaotic maps. Physical Review E 90:3.
Crossref
Rasmus Sloth Hansen & Steen Hannestad. (2014) Chaotic flavor evolution in an interacting neutrino gas. Physical Review D 90:2.
Crossref
Nikos Kyriakopoulos, Vassilis Koukouloyannis, Charalampos Skokos & Panayotis G. Kevrekidis. (2014) Chaotic behavior of three interacting vortices in a confined Bose-Einstein condensate. Chaos: An Interdisciplinary Journal of Nonlinear Science 24:2.
Crossref
Adrienne Norwood, Eugenia Kalnay, Kayo Ide, Shu-Chih Yang & Christopher Wolfe. (2013) Lyapunov, singular and bred vectors in a multi-scale system: an empirical exploration of vectors related to instabilities. Journal of Physics A: Mathematical and Theoretical 46:25, pages 254021.
Crossref
Luigi Palatella, Alberto Carrassi & Anna Trevisan. (2013) Lyapunov vectors and assimilation in the unstable subspace: theory and applications. Journal of Physics A: Mathematical and Theoretical 46:25, pages 254020.
Crossref
Pavel V Kuptsov. (2013) Violation of hyperbolicity via unstable dimension variability in a chain with local hyperbolic chaotic attractors. Journal of Physics A: Mathematical and Theoretical 46:25, pages 254016.
Crossref
Hong-liu Yang & Günter Radons. (2013) Hydrodynamic Lyapunov modes and effective degrees of freedom of extended systems. Journal of Physics A: Mathematical and Theoretical 46:25, pages 254015.
Crossref
D Pazó, J M López & M A Rodríguez. (2013) On the angle between the first and second Lyapunov vectors in spatio-temporal chaos. Journal of Physics A: Mathematical and Theoretical 46:25, pages 254014.
Crossref
H Bosetti & H A Posch. (2013) Orthogonal versus covariant Lyapunov vectors for rough hard disc systems. Journal of Physics A: Mathematical and Theoretical 46:25, pages 254011.
Crossref
Gary P Morriss & Daniel P Truant. (2013) A review of the hydrodynamic Lyapunov modes of hard disk systems. Journal of Physics A: Mathematical and Theoretical 46:25, pages 254010.
Crossref
Harald A Posch. (2013) Symmetry properties of orthogonal and covariant Lyapunov vectors and their exponents. Journal of Physics A: Mathematical and Theoretical 46:25, pages 254006.
Crossref
Francesco Ginelli, Hugues Chaté, Roberto Livi & Antonio Politi. (2013) Covariant Lyapunov vectors. Journal of Physics A: Mathematical and Theoretical 46:25, pages 254005.
Crossref
Gary Froyland, Thorsten Hüls, Gary P. Morriss & Thomas M. Watson. (2013) Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: A comparative numerical study. Physica D: Nonlinear Phenomena 247:1, pages 18-39.
Crossref
Hong‐Liu Yang & Günter Radons. 2013. Nonequilibrium Statistical Physics of Small Systems. Nonequilibrium Statistical Physics of Small Systems 361 391 .
Qiqi Wang. (2013) Forward and adjoint sensitivity computation of chaotic dynamical systems. Journal of Computational Physics 235, pages 1-13.
Crossref
E. Aykutlug, M. Maggia & K.D. Mease. (2013) Solving Partially Hyper-Sensitive Optimal Control Problems Using Manifold Structure. IFAC Proceedings Volumes 46:23, pages 187-192.
Crossref
Pavel V. Kuptsov & Ulrich Parlitz. (2012) Theory and Computation of Covariant Lyapunov Vectors. Journal of Nonlinear Science 22:5, pages 727-762.
Crossref
Nusret Balci, Anna L. Mazzucato, Juan M. Restrepo & George R. Sell. (2012) Ensemble Dynamics and Bred Vectors. Monthly Weather Review 140:7, pages 2308-2334.
Crossref
G. P. Morriss. (2012) Localization properties of covariant Lyapunov vectors for quasi-one-dimensional hard disks. Physical Review E 85:5.
Crossref
M. Romero-Bastida, Diego Pazó & Juan M. López. (2012) Covariant hydrodynamic Lyapunov modes and strong stochasticity threshold in Hamiltonian lattices. Physical Review E 85:2.
Crossref
Wm.G. Hoover & Carol G. Hoover. (2012) Local Gram–Schmidt and covariant Lyapunov vectors and exponents for three harmonic oscillator problems. Communications in Nonlinear Science and Numerical Simulation 17:2, pages 1043-1054.
Crossref
Pavel V. Kuptsov. (2012) Fast numerical test of hyperbolic chaos. Physical Review E 85:1.
Crossref
ANNA TREVISAN & LUIGI PALATELLA. (2012) CHAOS AND WEATHER FORECASTING: THE ROLE OF THE UNSTABLE SUBSPACE IN PREDICTABILITY AND STATE ESTIMATION PROBLEMS. International Journal of Bifurcation and Chaos 21:12, pages 3389-3415.
Crossref
Jason R. Green, Thomas S. Hofer, R. Stephen Berry & David J. Wales. (2011) Characterizing molecular motion in H2O and H3O+ with dynamical instability statistics. The Journal of Chemical Physics 135:18.
Crossref
Tony Chung, Daniel Truant & Gary P. Morriss. (2011) Lyapunov modes as fields. Physical Review E 83:4.
Crossref
Daniel P Truant & Gary P Morriss. (2011) The evolution of covariant Lyapunov modes in QOD hard disc systems. Journal of Statistical Mechanics: Theory and Experiment 2011:01, pages P01014.
Crossref
Diego Pazó & Juan M. López. (2010) Characteristic Lyapunov vectors in chaotic time-delayed systems. Physical Review E 82:5.
Crossref
Hadrien Bosetti, Harald A. Posch, Christoph Dellago & William G. Hoover. (2010) Time-reversal symmetry and covariant Lyapunov vectors for simple particle models in and out of thermal equilibrium. Physical Review E 82:4.
Crossref
Tony Chung, Daniel Truant & Gary P. Morriss. (2010) From Lyapunov modes to their exponents for hard disk systems. Physical Review E 81:6.
Crossref
Anna Trevisan, Massimo D'Isidoro & Olivier Talagrand. (2010) Four‐dimensional variational assimilation in the unstable subspace and the optimal subspace dimension. Quarterly Journal of the Royal Meteorological Society 136:647, pages 487-496.
Crossref
Jason R. Green, Julius Jellinek & R. Stephen Berry. (2009) Space-time properties of Gram-Schmidt vectors in classical Hamiltonian evolution. Physical Review E 80:6.
Crossref
Diego Pazó, Ivan G. Szendro, Juan M. López & Miguel A. Rodríguez. (2008) Structure of characteristic Lyapunov vectors in spatiotemporal chaos. Physical Review E 78:1.
Crossref
Christopher L. Wolfe & Roger M. Samelson. (2008) Singular Vectors and Time-Dependent Normal Modes of a Baroclinic Wave-Mean Oscillation. Journal of the Atmospheric Sciences 65:3, pages 875-894.
Crossref
Ivan G. Szendro, Diego Pazó, Miguel A. Rodríguez & Juan M. López. (2007) Spatiotemporal structure of Lyapunov vectors in chaotic coupled-map lattices. Physical Review E 76:2.
Crossref