American Institute of Mathematical Sciences

Advanced
February  2005, 12(2): 355-362. doi: 10.3934/dcds.2005.12.355

Shadowing in random dynamical systems

Lianfa He 1, , Hongwen Zheng 2, and  Yujun Zhu 1,

1. 

College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050016, China, China
2. 

Institute of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China

Received  August 2003 Revised  August 2004 Published  December 2004

In this paper we consider the shadowing property for $C^1$ random dynamical systems. We first define a type of hyperbolicity on the full measure invariant set which is given by Oseledec's multiplicative ergodic theorem, and then prove that the system has the "Lipschitz" shadowing property on it.
Keywords: multiplicative ergodic theorem, shadowing property., Random dynamical system.
Mathematics Subject Classification: 37C50, 37H9.
Citation: Lianfa He, Hongwen Zheng, Yujun Zhu. Shadowing in random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 355-362. doi: 10.3934/dcds.2005.12.355
[1]

Cecilia González-Tokman, Anthony Quas. A concise proof of the multiplicative ergodic theorem on Banach spaces. Journal of Modern Dynamics, 2015, 9: 237-255. doi: 10.3934/jmd.2015.9.237
[2]

Alex Blumenthal. A volume-based approach to the multiplicative ergodic theorem on Banach spaces. Discrete & Continuous Dynamical Systems - A, 2016, 36 (5) : 2377-2403. doi: 10.3934/dcds.2016.36.2377
[3]

Luciana A. Alves, Luiz A. B. San Martin. Multiplicative ergodic theorem on flag bundles of semi-simple Lie groups. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1247-1273. doi: 10.3934/dcds.2013.33.1247
[4]

Weigu Li, Kening Lu. Takens theorem for random dynamical systems. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3191-3207. doi: 10.3934/dcdsb.2016093
[5]

Junyi Tu, Yuncheng You. Random attractor of stochastic Brusselator system with multiplicative noise. Discrete & Continuous Dynamical Systems - A, 2016, 36 (5) : 2757-2779. doi: 10.3934/dcds.2016.36.2757
[6]

Weigu Li, Kening Lu. A Siegel theorem for dynamical systems under random perturbations. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 635-642. doi: 10.3934/dcdsb.2008.9.635
[7]

Xiangnan He, Wenlian Lu, Tianping Chen. On transverse stability of random dynamical system. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 701-721. doi: 10.3934/dcds.2013.33.701
[8]

Fang Zhang, Yunhua Zhou. On the limit quasi-shadowing property. Discrete & Continuous Dynamical Systems - A, 2017, 37 (5) : 2861-2879. doi: 10.3934/dcds.2017123
[9]

N. D. Cong, T. S. Doan, S. Siegmund. A Bohl-Perron type theorem for random dynamical systems. Conference Publications, 2011, 2011 (Special) : 322-331. doi: 10.3934/proc.2011.2011.322
[10]

Mariko Arisawa, Hitoshi Ishii. Some properties of ergodic attractors for controlled dynamical systems. Discrete & Continuous Dynamical Systems - A, 1998, 4 (1) : 43-54. doi: 10.3934/dcds.1998.4.43
[11]

Philippe Marie, Jérôme Rousseau. Recurrence for random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 1-16. doi: 10.3934/dcds.2011.30.1
[12]

Xiaoyue Li, Xuerong Mao. Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 523-545. doi: 10.3934/dcds.2009.24.523
[13]

Noriaki Kawaguchi. Topological stability and shadowing of zero-dimensional dynamical systems. Discrete & Continuous Dynamical Systems - A, 2019, 39 (5) : 2743-2761. doi: 10.3934/dcds.2019115
[14]

Yuri Kifer. Ergodic theorems for nonconventional arrays and an extension of the Szemerédi theorem. Discrete & Continuous Dynamical Systems - A, 2018, 38 (6) : 2687-2716. doi: 10.3934/dcds.2018113
[15]

Tao Jiang, Xianming Liu, Jinqiao Duan. Approximation for random stable manifolds under multiplicative correlated noises. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3163-3174. doi: 10.3934/dcdsb.2016091
[16]

Bixiang Wang. Random attractors for non-autonomous stochastic wave equations with multiplicative noise. Discrete & Continuous Dynamical Systems - A, 2014, 34 (1) : 269-300. doi: 10.3934/dcds.2014.34.269
[17]

Tomás Caraballo, José A. Langa, James C. Robinson. Stability and random attractors for a reaction-diffusion equation with multiplicative noise. Discrete & Continuous Dynamical Systems - A, 2000, 6 (4) : 875-892. doi: 10.3934/dcds.2000.6.875
[18]

Chi Phan. Random attractor for stochastic Hindmarsh-Rose equations with multiplicative noise. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2020060
[19]

Yujun Zhu. Preimage entropy for random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 829-851. doi: 10.3934/dcds.2007.18.829
[20]

Ji Li, Kening Lu, Peter W. Bates. Invariant foliations for random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2014, 34 (9) : 3639-3666. doi: 10.3934/dcds.2014.34.3639

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (30)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences