Constructing center-stable tori
Andy Hammerlindl
TL;DR
This paper demonstrates how weakly partially hyperbolic diffeomorphisms on the 2-torus can be embedded into higher-dimensional strongly partially hyperbolic systems with center-stable tori, and constructs such tori in higher dimensions.
Contribution
It introduces a method to realize 2D weakly partially hyperbolic dynamics within 3D strongly partially hyperbolic systems and provides new examples in higher dimensions.
Findings
Weakly partially hyperbolic diffeomorphisms on the 2-torus can be embedded into 3D systems.
Existence of center-stable and center-unstable tori in higher-dimensional systems.
Construction techniques for such tori in various dimensions.
Abstract
We show that any weakly partially hyperbolic diffeomorphism on the 2-torus may be realized as the dynamics on a center-stable or center-unstable torus of a 3-dimensional strongly partially hyperbolic system. We also construct examples of center-stable and center-unstable tori in higher dimensions.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Geometric and Algebraic Topology