August  2005, 5(3): 587-598. doi: 10.3934/dcdsb.2005.5.587

Bernoulli shift for second order recurrence relations near the anti-integrable limit

1. 

Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan

Received  September 2004 Revised  October 2004 Published  May 2005

We extend the anti-integrability theory of Aubry to non-autonomous twist maps between symplectic spaces to show the shift dynamics can be embedded in a natural way. Examples are given to illustrate that the embedded shift can be a full shift, a subshift of finite type or of infinite type.
Citation: Yi-Chiuan Chen. Bernoulli shift for second order recurrence relations near the anti-integrable limit. Discrete & Continuous Dynamical Systems - B, 2005, 5 (3) : 587-598. doi: 10.3934/dcdsb.2005.5.587
[1]

Thorsten Hüls, Yongkui Zou. On computing heteroclinic trajectories of non-autonomous maps. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 79-99. doi: 10.3934/dcdsb.2012.17.79

[2]

Thorsten Hüls. A model function for non-autonomous bifurcations of maps. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 351-363. doi: 10.3934/dcdsb.2007.7.351

[3]

José-Luis Bravo, Manuel Fernández. Limit cycles of non-autonomous scalar ODEs with two summands. Communications on Pure & Applied Analysis, 2013, 12 (2) : 1091-1102. doi: 10.3934/cpaa.2013.12.1091

[4]

Cung The Anh, Tang Quoc Bao. Dynamics of non-autonomous nonclassical diffusion equations on $R^n$. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1231-1252. doi: 10.3934/cpaa.2012.11.1231

[5]

Chunyou Sun, Daomin Cao, Jinqiao Duan. Non-autonomous wave dynamics with memory --- asymptotic regularity and uniform attractor. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 743-761. doi: 10.3934/dcdsb.2008.9.743

[6]

Wen Tan, Chunyou Sun. Dynamics for a non-autonomous reaction diffusion model with the fractional diffusion. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6035-6067. doi: 10.3934/dcds.2017260

[7]

Emma D'Aniello, Saber Elaydi. The structure of $ \omega $-limit sets of asymptotically non-autonomous discrete dynamical systems. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2019195

[8]

Alexandre N. Carvalho, José A. Langa, James C. Robinson. Non-autonomous dynamical systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (3) : 703-747. doi: 10.3934/dcdsb.2015.20.703

[9]

Xin Li, Chunyou Sun, Na Zhang. Dynamics for a non-autonomous degenerate parabolic equation in $\mathfrak{D}_{0}^{1}(\Omega, \sigma)$. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 7063-7079. doi: 10.3934/dcds.2016108

[10]

Xinguang Yang, Baowei Feng, Thales Maier de Souza, Taige Wang. Long-time dynamics for a non-autonomous Navier-Stokes-Voigt equation in Lipschitz domains. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 363-386. doi: 10.3934/dcdsb.2018084

[11]

Yun Lan, Ji Shu. Dynamics of non-autonomous fractional stochastic Ginzburg-Landau equations with multiplicative noise. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2409-2431. doi: 10.3934/cpaa.2019109

[12]

Dingshi Li, Kening Lu, Bixiang Wang, Xiaohu Wang. Limiting dynamics for non-autonomous stochastic retarded reaction-diffusion equations on thin domains. Discrete & Continuous Dynamical Systems - A, 2019, 39 (7) : 3717-3747. doi: 10.3934/dcds.2019151

[13]

Iacopo P. Longo, Sylvia Novo, Rafael Obaya. Topologies of continuity for Carathéodory delay differential equations with applications in non-autonomous dynamics. Discrete & Continuous Dynamical Systems - A, 2019, 39 (9) : 5491-5520. doi: 10.3934/dcds.2019224

[14]

Wenqiang Zhao. Smoothing dynamics of the non-autonomous stochastic Fitzhugh-Nagumo system on $\mathbb{R}^N$ driven by multiplicative noises. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3453-3474. doi: 10.3934/dcdsb.2018251

[15]

Maciej J. Capiński, Piotr Zgliczyński. Covering relations and non-autonomous perturbations of ODEs. Discrete & Continuous Dynamical Systems - A, 2006, 14 (2) : 281-293. doi: 10.3934/dcds.2006.14.281

[16]

Mark Comerford, Todd Woodard. Orbit portraits in non-autonomous iteration. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 2253-2277. doi: 10.3934/dcdss.2019144

[17]

Lorenzo Sella, Pieter Collins. Computation of symbolic dynamics for two-dimensional piecewise-affine maps. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 739-767. doi: 10.3934/dcdsb.2011.15.739

[18]

Snir Ben Ovadia. Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds. Journal of Modern Dynamics, 2018, 13: 43-113. doi: 10.3934/jmd.2018013

[19]

Xinyuan Liao, Caidi Zhao, Shengfan Zhou. Compact uniform attractors for dissipative non-autonomous lattice dynamical systems. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1087-1111. doi: 10.3934/cpaa.2007.6.1087

[20]

Joaquim P. Mateus, Paulo Rebelo, Silvério Rosa, César M. Silva, Delfim F. M. Torres. Optimal control of non-autonomous SEIRS models with vaccination and treatment. Discrete & Continuous Dynamical Systems - S, 2018, 11 (6) : 1179-1199. doi: 10.3934/dcdss.2018067

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]