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Experimental Mathematics Volume 11, 2002 - Issue 2
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Original Articles

Regularity of Conjugacies between Critical Circle Maps: An Experimental Study

Rafael de la Llave Department of Mathematics, University of Texas at Austin, Austin, TX, 78712 E-mail: [email protected]
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Nikola P. Petrov Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109 E-mail: [email protected]
Pages 219-241 | Published online: 03 Apr 2012

Citations (19)

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Timoteo Carletti. (2003) The 1/2-Complex Bruno Function and the Yoccoz Function: A Numerical Study of the Marmi-Moussa-Yoccoz Conjecture. Experimental Mathematics 12:4, pages 491-506.
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Articles from other publishers (18)

Armengol Gasull, Jorge Groisman & Francesc Mañosas. (2022) Regularization of Brouwer Translation Theorem. Qualitative Theory of Dynamical Systems 21:4.
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Joan Gimeno, Jiaqi Yang & Rafael de la Llave. (2021) Numerical Computation of Periodic Orbits and Isochrons for State-Dependent Delay Perturbation of an ODE in the Plane. SIAM Journal on Applied Dynamical Systems 20:3, pages 1514-1543.
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Lluís Alsedà i Soler, Josep Maria Mondelo González & David Romero i Sànchez. (2017) A numerical estimate of the regularity of a family of Strange Non-Chaotic Attractors. Physica D: Nonlinear Phenomena 347, pages 74-89.
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Renato Calleja & Jordi-Lluís Figueras. (2012) Collision of invariant bundles of quasi-periodic attractors in the dissipative standard map. Chaos: An Interdisciplinary Journal of Nonlinear Science 22:3.
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Rafael de la Llave & Alejandro Luque. (2011) Differentiability at the Tip of Arnold Tongues for Diophantine Rotations: Numerical Studies and Renormalization Group Explanations. Journal of Statistical Physics 143:6, pages 1154-1188.
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Renato Calleja & Rafael de la Llave. (2010) A numerically accessible criterion for the breakdown of quasi-periodic solutions and its rigorous justification. Nonlinearity 23:9, pages 2029-2058.
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Renato Calleja & Alessandra Celletti. (2010) Breakdown of invariant attractors for the dissipative standard map. Chaos: An Interdisciplinary Journal of Nonlinear Science 20:1.
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Alejandro Luque & Jordi Villanueva. (2009) Numerical computation of rotation numbers of quasi-periodic planar curves. Physica D: Nonlinear Phenomena 238:20, pages 2025-2044.
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Renato Calleja & Rafael de la Llave. (2009) Fast numerical computation of quasi-periodic equilibrium states in 1D statistical mechanics, including twist maps. Nonlinearity 22:6, pages 1311-1336.
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Alejandro Luque & Jordi Villanueva. (2008) Computation of derivatives of the rotation number for parametric families of circle diffeomorphisms. Physica D: Nonlinear Phenomena 237:20, pages 2599-2615.
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Rafael de la Llave & Nikola P. Petrov. (2008) Boundaries of Siegel disks: Numerical studies of their dynamics and regularity. Chaos: An Interdisciplinary Journal of Nonlinear Science 18:3.
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Arturo Olvera & Nikola P. Petrov. (2008) Regularity Properties of Critical Invariant Circles of Twist Maps, and Their Universality. SIAM Journal on Applied Dynamical Systems 7:3, pages 962-987.
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Rafael de la Llave, Arturo Olvera & Nikola P Petrov. (2007) Universal scalings of universal scaling exponents. Journal of Physics A: Mathematical and Theoretical 40:23, pages F427-F434.
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K. Fuchss, A. Wurm, A. Apte & P. J. Morrison. (2006) Breakup of shearless meanders and “outer” tori in the standard nontwist map. Chaos: An Interdisciplinary Journal of Nonlinear Science 16:3.
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Tere M. Seara & Jordi Villanueva. (2006) On the numerical computation of Diophantine rotation numbers of analytic circle maps. Physica D: Nonlinear Phenomena 217:2, pages 107-120.
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Alexander P. Kuznetsov, Sergey P. Kuznetsov & Julia V. Sedova. (2006) Effect of noise on the critical golden-mean quasiperiodic dynamics in the circle map. Physica A: Statistical Mechanics and its Applications 359, pages 48-64.
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Nikola P Petrov. (2005) The dynamical Casimir effect in a periodically changing domain: a dynamical systems approach. Journal of Optics B: Quantum and Semiclassical Optics 7:3, pages S89-S99.
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Nikola P. Petrov, Rafael de la Llave & John A. Vano. (2003) Torus maps and the problem of a one-dimensional optical resonator with a quasiperiodically moving wall. Physica D: Nonlinear Phenomena 180:3-4, pages 140-184.
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