Abstract:
Computer verification of hyperbolicity is provided based on statistical analysis of the angles of intersection of stable and unstable manifolds for mechanical systems with hyperbolic attractors of Smale – Williams type: (i) a particle sliding on a plane under periodic kicks, (ii) interacting particles moving on two alternately rotating disks, and (iii) a string with parametric excitation of standing-wave patterns by a modulated pump. The examples are of interest as contributing to filling the hyperbolic theory of dynamical systems with physical content.
Citation:
Sergey P. Kuznetsov, Vyacheslav P. Kruglov, “Verification of Hyperbolicity for Attractors of Some Mechanical Systems with Chaotic Dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 160–174
\Bibitem{KuzKru16}
\by Sergey P. Kuznetsov, Vyacheslav P. Kruglov
\paper Verification of Hyperbolicity for Attractors of Some Mechanical Systems with Chaotic Dynamics
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 2
\pages 160--174
\mathnet{http://mi.mathnet.ru/rcd72}
\crossref{https://doi.org/10.1134/S1560354716020027}
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Linking options:
https://www.mathnet.ru/eng/rcd72
https://www.mathnet.ru/eng/rcd/v21/i2/p160
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Miguel A. Prado Reynoso, Marcus W. Beims, “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 (2022), 106358
M. A. Prado Reynoso, R. M. da Silva, M. W. Beims, “Studying partial hyperbolicity inside regimes of motion in Hamiltonian systems”, Chaos Solitons Fractals, 144 (2021), 110640
S. V. Gonchenko, D. V. Turaev, A. O. Kazakov, M. H. Kaynov, “On Methods For Verification of the Pseudohyperbolicity of Strange Attractors”, Izv. Vyss. Uchebn. Zaved.-Prikl. Nelineynaya Din., 29:1 (2021), 160–185
Yu. V. Bakhanova, A. O. Kazakov, E. Yu. Karatetskaia, A. D. Kozlov, K. A. Safonov, “On homoclinic attractors of three-dimensional flows”, Izv. Vyss. Uchebn. Zaved.-Prikl. Nelineynaya Din., 28:3 (2020), 231–258
S. P. Kuznetsov, V. P. Kruglov, “Hyperbolic chaos in a system of two Froude pendulums with alternating periodic braking”, Commun. Nonlinear Sci. Numer. Simul., 67 (2019), 152–161
P. V. Kuptsov, S. P. Kuznetsov, “Numerical test for hyperbolicity in chaotic systems with multiple time delays”, Commun. Nonlinear Sci. Numer. Simul., 56 (2018), 227–239
V. M. Doroshenko, V. P. Kruglov, S. P. Kuznetsov, “Smale – Williams Solenoids in a System of Coupled Bonhoeffer – van der Pol Oscillators”, Nelin. Dinam., 14:4 (2018), 435–451
V. M. Doroshenko, V. P. Kruglov, S. P. Kuznetsov, “Generator khaosa s attraktorom Smeila–Vilyamsa na osnove effekta gibeli kolebanii”, Nelineinaya dinam., 13:3 (2017), 303–315
V. M. Doroshenko, V. P. Kruglov, M. V. Pozdnyakov, “Robust chaos in systems of circular geometry”, 2017 Progress In Electromagnetics Research Symposium - Spring (PIERS), IEEE, 2017, 3122–3128
P. V. Kuptsov, S. P. Kuznetsov, “Numerical test for hyperbolicity of chaotic dynamics in time-delay systems”, Phys. Rev. E, 94:1 (2016), 010201
S. P. Kuznetsov, “Ot dinamiki Anosova na poverkhnosti otritsatelnoi krivizny k elektronnomu generatoru grubogo khaosa”, Izv. Sarat. un-ta. Nov. cer. Ser. Fizika, 16:3 (2016), 131–144
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