American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Pullback attractors and statistical solutions for 2-D Navier-Stokes equations
  • DCDS-B Home
  • This Issue
  • Next Article
    Center manifolds and dynamics near equilibria of quasilinear parabolic systems with fully nonlinear boundary conditions
May  2008, 9(3&4, May): 635-642. doi: 10.3934/dcdsb.2008.9.635

A Siegel theorem for dynamical systems under random perturbations

Weigu Li 1, and  Kening Lu 2,

1. 

School of Mathematics, Peking University, Beijing 100871, China
2. 

Department of Mathematics, Brigham Young University, Provo, Utah 84602

Received  January 2007 Revised  July 2007 Published  February 2008

In this paper, we generalize the classical Siegel’s theorem for deterministic dynamical systems to that under random perturbations.
Keywords: Random dynamical systems, Siegel's theorem..
Mathematics Subject Classification: Primary: 60H15; Secondary: 37H05, 37L55, 37L25, 37D1.
Citation: 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
[1]

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
[2]

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
[3]

Lianfa He, Hongwen Zheng, Yujun Zhu. Shadowing in random dynamical systems. Discrete & Continuous Dynamical Systems, 2005, 12 (2) : 355-362. doi: 10.3934/dcds.2005.12.355
[4]

Philippe Marie, Jérôme Rousseau. Recurrence for random dynamical systems. Discrete & Continuous Dynamical Systems, 2011, 30 (1) : 1-16. doi: 10.3934/dcds.2011.30.1
[5]

Hahng-Yun Chu, Se-Hyun Ku, Jong-Suh Park. Conley's theorem for dispersive systems. Discrete & Continuous Dynamical Systems - S, 2015, 8 (2) : 313-321. doi: 10.3934/dcdss.2015.8.313
[6]

Zhiming Li, Lin Shu. The metric entropy of random dynamical systems in a Hilbert space: Characterization of invariant measures satisfying Pesin's entropy formula. Discrete & Continuous Dynamical Systems, 2013, 33 (9) : 4123-4155. doi: 10.3934/dcds.2013.33.4123
[7]

Yujun Zhu. Preimage entropy for random dynamical systems. Discrete & Continuous Dynamical Systems, 2007, 18 (4) : 829-851. doi: 10.3934/dcds.2007.18.829
[8]

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

Björn Schmalfuss. Attractors for nonautonomous and random dynamical systems perturbed by impulses. Discrete & Continuous Dynamical Systems, 2003, 9 (3) : 727-744. doi: 10.3934/dcds.2003.9.727
[10]

Ivan Werner. Equilibrium states and invariant measures for random dynamical systems. Discrete & Continuous Dynamical Systems, 2015, 35 (3) : 1285-1326. doi: 10.3934/dcds.2015.35.1285
[11]

Yuri Kifer. Computations in dynamical systems via random perturbations. Discrete & Continuous Dynamical Systems, 1997, 3 (4) : 457-476. doi: 10.3934/dcds.1997.3.457
[12]

Thomas Bogenschütz, Achim Doebler. Large deviations in expanding random dynamical systems. Discrete & Continuous Dynamical Systems, 1999, 5 (4) : 805-812. doi: 10.3934/dcds.1999.5.805
[13]

Giovanni Forni, Howard Masur, John Smillie. Bill Veech's contributions to dynamical systems. Journal of Modern Dynamics, 2019, 14: v-xxv. doi: 10.3934/jmd.2019v
[14]

Armengol Gasull, Víctor Mañosa. Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 651-670. doi: 10.3934/dcdsb.2019259
[15]

Oliver Díaz-Espinosa, Rafael de la Llave. Renormalization and central limit theorem for critical dynamical systems with weak external noise. Journal of Modern Dynamics, 2007, 1 (3) : 477-543. doi: 10.3934/jmd.2007.1.477
[16]

Doan Thai Son. On analyticity for Lyapunov exponents of generic bounded linear random dynamical systems. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3113-3126. doi: 10.3934/dcdsb.2017166
[17]

T. Jäger. Neuronal coding of pacemaker neurons -- A random dynamical systems approach. Communications on Pure & Applied Analysis, 2011, 10 (3) : 995-1009. doi: 10.3934/cpaa.2011.10.995
[18]

Anhui Gu. Asymptotic behavior of random lattice dynamical systems and their Wong-Zakai approximations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5737-5767. doi: 10.3934/dcdsb.2019104
[19]

Xianfeng Ma, Ercai Chen. Pre-image variational principle for bundle random dynamical systems. Discrete & Continuous Dynamical Systems, 2009, 23 (3) : 957-972. doi: 10.3934/dcds.2009.23.957
[20]

Kening Lu, Alexandra Neamţu, Björn Schmalfuss. On the Oseledets-splitting for infinite-dimensional random dynamical systems. Discrete & Continuous Dynamical Systems - B, 2018, 23 (3) : 1219-1242. doi: 10.3934/dcdsb.2018149

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (64)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences