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Original Articles

Informal Remarks on the Orbit Structure of Discrete Approximations to Chaotic Maps

Pages 317-324 | Published online: 03 Apr 2012

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Pierre-Antoine Guihéneuf & Maurizio Monge. (2023) Cramér distance and discretizations of circle expanding maps II: simulations. Dynamical Systems 0:0, pages 1-33.
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Oleg Garasym, Jean-Pierre Lozi & René Lozi. (2017) How useful randomness for cryptography can emerge from multicore-implemented complex networks of chaotic maps. Journal of Difference Equations and Applications 23:5, pages 821-859.
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Articles from other publishers (29)

Pierre-Antoine Guihéneuf & Maurizio Monge. (2023) Cramér distance and discretisations of circle expanding maps I: theory. Nonlinearity 36:9, pages 4810-4843.
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M. Pollicott & P. Vytnova. (2022) Accurate Bounds on Lyapunov Exponents for Expanding Maps of the Interval. Communications in Mathematical Physics 397:1, pages 485-502.
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Chunyuan Liu & Qun Ding. (2020) A Color Image Encryption Scheme Based on a Novel 3D Chaotic Mapping. Complexity 2020, pages 1-20.
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Bruce N Roth & Michael Wilkinson. (2020) Numerical coalescence of chaotic trajectories. Journal of Physics A: Mathematical and Theoretical 53:34, pages 345701.
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Chunyuan Liu & Qun Ding. (2020) A Modified Algorithm for the Logistic Sequence Based on PCA. IEEE Access 8, pages 45254-45262.
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Dragan Lambić, Aleksandar Janković & Musheer Ahmad. (2018) Security Analysis of the Efficient Chaos Pseudo-random Number Generator Applied to Video Encryption. Journal of Electronic Testing 34:6, pages 709-715.
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Mohamed Lamine Sahari & Ibtissem Boukemara. (2018) A pseudo-random numbers generator based on a novel 3D chaotic map with an application to color image encryption. Nonlinear Dynamics 94:1, pages 723-744.
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Fadi Antown, Davor Dragičević & Gary Froyland. (2018) Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems. Journal of Statistical Physics 170:6, pages 1051-1087.
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Dragan Lambić. (2017) Security analysis of the pseudo-random bit generator based on multi-modal maps. Nonlinear Dynamics 91:1, pages 505-513.
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O. Jenkinson, M. Pollicott & P. Vytnova. (2017) Rigorous Computation of Diffusion Coefficients for Expanding Maps. Journal of Statistical Physics 170:2, pages 221-253.
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Jean-Pierre Lozi, Oleg Garasym & René Lozi. 2017. Industrial Mathematics and Complex Systems. Industrial Mathematics and Complex Systems 43 76 .
Wael Bahsoun, Stefano Galatolo, Isaia Nisoli & Xiaolong Niu. (2016) Rigorous Approximation of Diffusion Coefficients for Expanding Maps. Journal of Statistical Physics 163:6, pages 1486-1503.
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Oleg Garasym, Ren? Lozi & Ina Taralova. (2016) Robust PRNG based on homogeneously distributed chaotic dynamics. Journal of Physics: Conference Series 692, pages 012011.
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Oleg Garasym, Ina Taralova & René Lozi. 2016. Complex Systems and Networks. Complex Systems and Networks 131 161 .
Stefano Galatolo, Isaia Nisoli & Beno?t Saussol. (2015) An elementary way to rigorously estimate convergence to equilibrium and escape rates. Journal of Computational Dynamics 2:1, pages 51-64.
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PIERRE-ANTOINE GUIHÉNEUF. (2014) Dynamical properties of spatial discretizations of a generic homeomorphism. Ergodic Theory and Dynamical Systems 35:5, pages 1474-1523.
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René Lozi. 2015. Mathematical Models, Methods and Applications. Mathematical Models, Methods and Applications 1 30 .
STEFANO GALATOLO, ISAIA NISOLI & CRISTÓBAL ROJAS. (2014) Probability, statistics and computation in dynamical systems. Mathematical Structures in Computer Science 24:3.
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Stefano Galatolo & Isaia Nisoli. (2014) An Elementary Approach to Rigorous Approximation of Invariant Measures. SIAM Journal on Applied Dynamical Systems 13:2, pages 958-985.
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R. LOZI. (2012) EMERGENCE OF RANDOMNESS FROM CHAOS. International Journal of Bifurcation and Chaos 22:02, pages 1250021.
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Stefano Galatolo, Mathieu Hoyrup & Crist?bal Rojas. (2011) Statistical properties of dynamical systems ? Simulation and abstract computation. Chaos, Solitons & Fractals.
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István Scheuring & Gábor Domokos. (2007) Only noise can induce chaos in discrete populations. Oikos 116:3, pages 361-366.
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GÁBOR DOMOKOS. (2011) COARSE-GRAINED OBSERVATION OF DISCRETIZED MAPS. International Journal of Bifurcation and Chaos 15:03, pages 861-870.
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Istv?n Scheuring & G?bor Domokos. (2005) Sturdy cycles in the chaotic Tribolium castaneum data series. Theoretical Population Biology 67:2, pages 127-139.
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P.-M. Binder & Nicholas H. Okamoto. (2005) Noisy integer maps. Physica A: Statistical Mechanics and its Applications 347, pages 51-64.
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Anthony D. Rosato, Denis Blackmore, Liam Buckley, Christopher Oshman & Mark Johnson. (2004) Experimental, Simulation and Nonlinear Dynamics of Galton's Board. International Journal of Nonlinear Sciences and Numerical Simulation 5:4.
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P. DIAMOND & I. VLADIMIROV. (2011) BRANCHING PROCESSES AND COMPUTATIONAL COLLAPSE OF DISCRETIZED UNIMODAL MAPPINGS. International Journal of Bifurcation and Chaos 12:12, pages 2847-2867.
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Christoph Dellago & Wm. G. Hoover. (2000) Finite-precision stationary states at and away from equilibrium. Physical Review E 62:5, pages 6275-6281.
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Igor Vladimirov, Nikolai Kuznetsov & Phil Diamond. (2000) Frequency measurability, algebras of quasiperiodic sets and spatial discretizations of smooth dynamical systems. Mathematics and Computers in Simulation 52:3-4, pages 251-272.
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