Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I. General theory
DOI10.1090/S0002-9947-2013-05814-XzbMath1350.37061arXiv1209.3475MaRDI QIDQ2847197
Wenxian Shen, Janusz Mierczyński
Publication date: 4 September 2013
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1209.3475
Lyapunov exponentrandom dynamical systemordered Banach spacemultiplicative ergodic theoremskew-product semiflowHilbert projective metricexponential separationprincipal Floquet subspaces
Ordinary differential equations and systems with randomness (34F05) Ergodic theorems, spectral theory, Markov operators (37A30) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Infinite-dimensional random dynamical systems; stochastic equations (37L55)
Related Items (19)
Cites Work
- A proof of Oseledec's multiplicative ergodic theorem
- Spectral theory for general nonautonomous/random dispersal evolution operators
- Time averaging for nonautonomous/random linear parabolic equations
- Ergodic theorems. With a supplement by Antoine Brunel
- Ergodic theory of differentiable dynamical systems
- Analycity properties of the characteristic exponents of random matrix products
- Characteristic exponents and invariant manifolds in Hilbert space
- Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems
- Globally positive solutions of linear parabolic partial differential equations of second order with Dirichlet boundary conditions
- Evolutionary formalism for products of positive random matrices
- Globally positive solutions of linear parabolic PDEs of second order with Robin boundary conditions
- Invariant manifolds for stochastic partial differential equations.
- Monotone random systems theory and applications
- The principal Floquet bundle and exponential separation for linear parabolic equations
- On uniqueness of positive entire solutions and other properties of linear parabolic equations
- The principal spectrum for linear nonautonomous parabolic PDEs of second order: Basic properties
- Exponential separation and principal Lyapunov exponent/spectrum for random/nonautonomous parabolic equations
- Decay of correlations
- Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations
- Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations
- Harnack inequality and exponential separation for oblique derivative problems on Lipschitz domains
- Estimates for the principal spectrum point for certain time-dependent parabolic operators
- A multiplicative ergodic theorem with applications to a first order stochastic hyperbolic equation in a bounded domain
- Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space
- Ergodic Properties of Linear Dynamical Systems
- Hilbert’s projective metric and iterated nonlinear maps
- Positive Cones and Focal Points for a Class of nth Order Differential Equations
- Almost automorphic and almost periodic dynamics in skew-product semiflows
- Hilbert's Projective Metric and the Spectral Properties of Positive Linear Operators
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I. General theory