PERIODICITY AND SHARKOVSKY'S THEOREM FOR RANDOM DYNAMICAL SYSTEMS

DOI10.1142/S0219493701000199zbMath1064.37037MaRDI QIDQ4460424

Marc Klünger

Publication date: 18 May 2004

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Combinatorial dynamics (types of periodic orbits) (37E15) Low-dimensional dynamical systems (37E99) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05) General theory of random and stochastic dynamical systems (37H05) One-parameter continuous families of measure-preserving transformations (28D10)

Related Items (12)

Asymptotic behaviors of stochastic periodic differential equation with Markovian switching ⋮ On degenerate backward SPDEs in bounded domains under non-local conditions ⋮ On backward SPDEs without proper Cauchy condition ⋮ Random periodic processes, periodic measures and ergodicity ⋮ Random periodic solutions of SPDEs via integral equations and Wiener-Sobolev compact embedding ⋮ Coexistence of Random Subharmonic Solutions of Random Impulsive Differential Equations and Inclusions on a Circle ⋮ Randomization of Sharkovsky-type results on the circle ⋮ The Sharkovskiĭ Theorem for spaces of measurable functions ⋮ Randomization of Sharkovskii-type theorems ⋮ Randomized Sharkovsky-type results and random subharmonic solutions of differential inclusions ⋮ Application of the randomized Sharkovsky-type theorems to random impulsive differential equations and inclusions ⋮ On forward and backward SPDEs with non-local boundary conditions

Cites Work

• Random walks on compact groups and the existence of cocycles
• Random perturbations of Axiom A basic sets
• Topological fixed point theorems do not hold for random dynamical systems
• Period Three Implies Chaos

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