Palestras e Seminários
30/10/2024
14:00
online / à distância
Palestrante: Piotr Kalita
https://sites.google.com/usp.br/evol-eq-and-dyn-systems
Responsável: Estefani Moraes Moreira (estefani@usp.br)
Webinar on Evolution Equations and Dynamical Systems
Abstract: We consider the problem governed by the gradient ODE $x'=\nabla F(x)$ in $\mathbb{R}^d$ on which we assume that it has a finite number of hyperbolic equilibria whose stable and unstable manifolds intersect transversally. The problem is perturbed by the memory term $x'=\nabla F(x) + \varepsilon\int_{-\infty}^t M(t-s)x(s)\, ds$ where $\varepsilon>0$ and $M(s)$ decay exponentially. The key result is that the structure of connections between the equilibria of the unperturbed problem is exactly preserved in the infinite dimensional dynamical system for a small $\varepsilon > 0$. The talk is based on a preprint https://arxiv.org/abs/2406.
Link: No SITE