.png){kind=icon}
.png){kind=icon}
Return
DISSERTATION ES MATHEMATICAE
.png){kind=icon}
PRE
AI
DOI：10.4064/dm240812-6-5.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
We investigate the existence and regularity of locally invariant manifolds near an approximately invariant set that satisfies a geometric hyperbolicity condition with respect to an abstract "generalized" dynamical system in Banach spaces. This hyperbolicity framework, which we term partial normal hyperbolicity, bridges the gap between normal hyperbolicity and partial hyperbolicity-concepts previously studied in finite dimensions and specific PDE contexts. Our generalized dynamical system accommodates non-smooth, non-Lipschitz, and even "non-mapping" dynamics, making it applicable to both well-posed and ill-posed differential equations. As an illustrative application, we employ our results to analyze the dynamics of whiskered tori.
Keywords:
invariant manifold
partially normal hyperbolicity
infinite-dimensional dynamical system
ill-posed differential equation
whiskered torus