08/09/2022, 09:45 — 10:30 — Abreu Faro Amphitheatre
Alexandre Carvalho, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos

Inertial Manifolds, Saddle Point Property and Exponential Dichotomy: A unified theory

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.

See also

Alexandre_Carvalho_ISTIME_2022.pdf