TOWARDS A MORSE THEORY FOR RANDOM DYNAMICAL SYSTEMS

DOI10.1142/S0219493704001073zbMath1050.37026MaRDI QIDQ4822529

Hans Crauel, Luu Hoang Duc, Stefan Siegmund

Publication date: 25 October 2004

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

zbMATH Keywords

Morse theoryattractor-repeller pairMorse decompositionMorse set

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Index theory for dynamical systems, Morse-Conley indices (37B30) Random dynamical systems (37H99) Stability of manifolds of solutions to ordinary differential equations (34D35)

Related Items (12)

The echo index and multistability in input-driven recurrent neural networks ⋮ Morse decompositions of nonautonomous dynamical systems ⋮ Morse decompositions for periodic general dynamical systems and differential inclusions ⋮ Measure attractors and Markov attractors ⋮ Strong Morse–Lyapunov functions for Morse decompositions of attractors of random dynamical systems ⋮ Morse decompositions for nonautonomous general dynamical systems ⋮ On the Morse theory of attractors: a functional approach ⋮ Nonautonomous and random attractors ⋮ ATTRACTOR–REPELLER PAIR, MORSE DECOMPOSITION AND LYAPUNOV FUNCTION FOR RANDOM DYNAMICAL SYSTEMS ⋮ Morse decompositions of uniform random attractors ⋮ Criteria for strong and weak random attractors ⋮ Random chain recurrent sets for random dynamical systems

Cites Work

• Morse decompositions in the absence of uniqeness.
• Attractors for random dynamical systems
• Random attractors
• The random attractor of the stochastic Lorenz system
• Conley index continuation for singularly perturbed hyperbolic equations
• Comparison of various concepts of a random attractor: a case study
• A uniformly exponential random forward attractor which is not a pullback attractor
• Random Point Attractors Versus Random Set Attractors
• Random attractors for the 3d stochastic navier-stokes equation with multiplicative white noise
• Convergence to local random attractors

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