A remark on the topological stability of symplectomorphisms
Mario Bessa, Jorge Rocha
TL;DR
This paper establishes that within the space of C1 symplectomorphisms, the topologically stable ones are necessarily Anosov, highlighting a strong link between stability and hyperbolic structure in symplectic dynamics.
Contribution
It proves that the C1 interior of topologically stable symplectomorphisms coincides with Anosov symplectomorphisms, clarifying their relationship.
Findings
Topologically stable C1 symplectomorphisms are Anosov.
The C1 interior of topologically stable symplectomorphisms is contained in the set of Anosov symplectomorphisms.
Provides a characterization of stability in symplectic dynamics.
Abstract
We prove that the C1 interior of the set of all topologically stable C1 symplectomorphisms is contained in the set of Anosov symplectomorphisms.
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 · Geometric and Algebraic Topology · Advanced Mathematical Theories and Applications