The dichotomy spectrum for random dynamical systems and pitchfork bifurcations with additive noise

DOI10.1214/16-AIHP763zbMath1383.37037arXiv1310.6166OpenAlexW1659900367MaRDI QIDQ1700382

Jeroen S. W. Lamb, Martin Rasmussen, Thai Son Doan, Mark Callaway

Publication date: 5 March 2018

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.6166

zbMATH Keywords

topological equivalencerandom dynamical systempitchfork bifurcationfinite-time Lyapunov exponent

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Bifurcation theory for random and stochastic dynamical systems (37H20)

Related Items (15)

Bifurcations in Asymptotically Autonomous Hamiltonian Systems Subject to Multiplicative Noise ⋮ Hopf bifurcation with additive noise ⋮ On the pitchfork bifurcation for the Chafee-Infante equation with additive noise ⋮ Long-Term Behaviour of Asymptotically Autonomous Hamiltonian Systems with Multiplicative Noise ⋮ Additive noise destroys the random attractor close to bifurcation ⋮ Bifurcation Theory for SPDEs: Finite-time Lyapunov Exponents and Amplitude Equations ⋮ Attractors. Then and now ⋮ A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits ⋮ Stochastic Sensitivity: A Computable Lagrangian Uncertainty Measure for Unsteady Flows ⋮ Bifurcation in Mean Phase Portraits for Stochastic Dynamical Systems with Multiplicative Gaussian Noise ⋮ Conditioned Lyapunov exponents for random dynamical systems ⋮ Bautin bifurcation with additive noise ⋮ Ruelle-Pollicott resonances of stochastic systems in reduced state space. Part II: Stochastic Hopf bifurcation ⋮ The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor ⋮ Continuity and topological structural stability for nonautonomous random attractors

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonautonomous and random attractors
• Maximal Lyapunov exponents for random matrix products
• Dichotomy spectra and Morse decompositions of linear nonautonomous differential equations
• A characterization of exponential dichotomy in terms of topological equivalence
• A spectral theory for linear differential systems
• Additive noise destroys a pitchfork bifurcation
• A stochastic Hopf bifurcation
• Attractors for random dynamical systems
• Lagrangian coherent structures and mixing in two-dimensional turbulence
• Stochastic bifurcation of pathwise random almost periodic and almost automorphic solutions for random dynamical systems
• Some characterizations of normal and perfectly normal spaces
• The dichotomy spectrum for noninvertible systems of linear difference equations
• Sternberg theorems for random dynamical systems
• THE COHOMOLOGY OF STOCHASTIC AND RANDOM DIFFERENTIAL EQUATIONS, AND LOCAL LINEARIZATION OF STOCHASTIC FLOWS
• Ergodic Properties of Linear Dynamical Systems
• Random attractors for the 3d stochastic navier-stokes equation with multiplicative white noise
• An alternative approach to Sacker–Sell spectral theory
• Stochastic bifurcation
• The conjugacy of stochastic and random differential equations and the existence of global attractors
• Dichotomy spectrum for nonautonomous differential equations

This page was built for publication: The dichotomy spectrum for random dynamical systems and pitchfork bifurcations with additive noise