Existence of SRB Measures for A Class of Partially Hyperbolic Attractors in Banach spaces
Zeng Lian, Peidong Liu, and Kening Lu
TL;DR
This paper proves that certain infinite-dimensional dynamical systems with partially hyperbolic attractors possess SRB measures, extending the understanding of statistical properties in Banach space dynamics.
Contribution
It establishes the existence of SRB measures for a class of infinite-dimensional systems with partially hyperbolic attractors, a novel result in Banach space dynamics.
Findings
SRB measures exist for systems with finite-dimensional unstable directions
Partially hyperbolic attractors guarantee SRB measures in Banach spaces
Extends finite-dimensional dynamical systems theory to infinite-dimensional settings
Abstract
In this paper, we study the existence of SRB measures for infinite dimensional dynamical systems in a Banach space. We show that if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has an SRB measure.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Stability and Controllability of Differential Equations · Quantum chaos and dynamical systems