A unified theory for inertial manifolds, saddle point property and exponential dichotomy

Invariant manifold theory for dynamical systems (37D10) Hyperbolicity, Lyapunov functions for infinite-dimensional dissipative dynamical systems (37L45) Inertial manifolds (35B42) Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems (37L25)

Cites Work

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Attractors for infinite-dimensional non-autonomous dynamical systems
A sharp condition for existence of an inertial manifold
Non-autonomous perturbation of autonomous semilinear differential equations: continuity of local stable and unstable manifolds
Regularity of invariant manifolds for nonuniformly hyperbolic dynamics
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Inertial manifolds for nonlinear evolutionary equations
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Smoothness of inertial manifolds
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Dichotomies in stability theory
Exponential dichotomy and mild solutions of nonautonomous equations in Banach spaces
A scalar parabolic equation whose asymptotic behavior is dictated by a system of ordinary differential equations
Die Stabilitätsfrage bei Differentialgleichungen.
Pullback attracting inertial manifolds for nonautonomous dynamical systems
Lipschitz perturbations of Morse-Smale semigroups
Robustness of noninvertible dichotomies
Dichotomies and reducibility
Linear differential equations and functional analysis. I
Linear differential equations and functional analysis. III: Lyapunov's second method in the case of conditional stability
Norms and determinants of linear mappings
Abstract Parabolic Evolution Equations and their Applications
Numbers of zeros on invariant manifolds in reaction- diffusion equations
Attractors Under Autonomous and Non-autonomous Perturbations
Inertial manifolds and finite-dimensional reduction for dissipative PDEs
Analytic semigroups and optimal regularity in parabolic problems

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