Orbit growth of contact structures after surgery

Autor: Anne Vaugon, Boris Hasselblatt, Patrick Foulon

Publikováno v: Annales Henri Lebesgue. 4:1103-1141

This work is at the intersection of dynamical systems and contact geometry, and it focuses on the effects of a contact surgery adapted to the study of Reeb fields and on the effects of invariance of contact homology. We show that this contact surgery

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5e9336aa7059182d2a11b54ce1c2ba0a
https://doi.org/10.5802/ahl.98

Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$

Autor: Wolfgang Ziller, Vladimir S. Matveev, Patrick Foulon, Sergei Ivanov, Robert L. Bryant

Publikováno v: J. Differential Geom. 117, no. 1 (2021), 1-22
Journal of Differential Geometry
Journal of Differential Geometry, In press, 117 (1), pp.1-22. ⟨10.4310/jdg/1609902015⟩
Journal of Differential Geometry, International Press, In press, 117 (1), pp.1-22. ⟨10.4310/jdg/1609902015⟩
Journal of Differential Geometry, International Press, In press

International audience; We study non-reversible Finsler metrics with constant flag curvature 1 on S 2 and show that the geodesic flow of every such metric is conjugate to that of one of Katok's examples, which form a 1-parameter family. In particular

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b3c3cba72e2e57542e32849b936c8c39
https://projecteuclid.org/euclid.jdg/1609902015

Zermelo deformation of Finsler metrics by Killing vector fields

Autor: Patrick Foulon, Vladimir S. Matveev

Publikováno v: Communications in Mathematical Sciences
Communications in Mathematical Sciences, International Press, 2018, 25, pp.1935-9179. ⟨10.3934/era.2018.25.001⟩
Communications in Mathematical Sciences, 2018, 25, pp.1935-9179. ⟨10.3934/era.2018.25.001⟩

International audience; We show how geodesics, Jacobi vector fields, and flag curvature of a Finsler metric behave under Zermelo deformation with respect to a Killing vector field. We also show that Zermelo deformation with respect to a Killing vecto

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::91799f2c44de2aa5586b702c243f422d
http://arxiv.org/abs/1710.01281

Longitudinal foliation rigidity and Lipschitz-continuous invariant forms for hyperbolic flows

Autor: Patrick Foulon, Boris Hasselblatt, Yong Fang

Publikováno v: Electronic Research Announcements in Mathematical Sciences. 17:80-89

In several contexts the defining invariant structures of a hyperbolic dynamical system are smooth only in systems of algebraic origin, and we prove new results of this smooth rigidity type for a class of flows.   For a transversely symplectic uni

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b28078fea3ba55d27cf0f6c50e36aa26
https://doi.org/10.3934/era.2010.17.80

Lipschitz continuous invariant forms for algebraic Anosov systems

Autor: Patrick Foulon, Boris Hasselblatt

Publikováno v: Journal of Modern Dynamics. 4:571-584

We prove results for algebraic Anosov systems that imply smoothness and a special structure for any Lipschitz continuous invariant $1$-form. This has corollaries for rigidity of time-changes, and we give a particular application to geometric rigidity

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::867b57ee82736340e1ff9efc106ab341
https://doi.org/10.3934/jmd.2010.4.571