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arXiv · 2111.11469

A Unified Theory for Inertial Manifolds, Saddle Point Property and Exponential Dichotomy

Alexandre N. Carvalho·Phillipo Lappicy·Estefani M. Moreira·Alexandre N. Oliveira-Sousa
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Abstract

Inertial manifold theory, saddle point property and exponential dichotomy have been treated as different topics in the literature with different proofs. As a common feature, they all have the purpose of `splitting' the space to understand the dynamics. We present a unified proof for the inertial manifold theorem, which as a local consequence yields the saddle-point property with a fine structure of invariant manifolds and the roughness of exponential dichotomy. In particular, we use these tools in order to establish the hyperbolicity of certain global solutions for non-autonomous parabolic partial differential equations.

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Alexandre N. Carvalho, Phillipo Lappicy, Estefani M. Moreira, Alexandre N. Oliveira-Sousa. 2021-11-22. A Unified Theory for Inertial Manifolds, Saddle Point Property and Exponential Dichotomy. https://arxiv.org/abs/2111.11469

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