Skip to Main content Skip to Navigation
Theses

Asymptotic Maslov indices

Abstract : We study the asymptotic Maslov index for surface diffeomorphisms. Roughly speaking, this quantity is the limit of the average rotational velocity of tangent vectors which evolve under the action of the differential of the diffeomorphism. For twist maps on the annulus, we prove that the set of points of zero index has Hausdorff dimension at least one. In the framework of conservative twist maps, we show that every bounded instability region has a positive Lebesgue measure set of points with non zero index. Finally, we study such index in the presence of periodic hyperbolic points with transverse homoclinic intersections, providing examples of points at which the asymptotic Maslov index does not exist.
Document type :
Theses
Complete list of metadatas

Cited literature [91 references]  Display  Hide  Download

https://hal-univ-avignon.archives-ouvertes.fr/tel-02363202
Contributor : Anna Florio <>
Submitted on : Thursday, November 14, 2019 - 11:59:11 AM
Last modification on : Wednesday, March 11, 2020 - 1:20:12 AM
Long-term archiving on: : Saturday, February 15, 2020 - 2:47:35 PM

File

theseFLORIO.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : tel-02363202, version 1

Collections

Citation

Anna Florio. Asymptotic Maslov indices. Dynamical Systems [math.DS]. Avignon Université, 2019. English. ⟨tel-02363202v1⟩

Share

Metrics

Record views

44

Files downloads

25