English
The spectral norm, rigidity and all that
Multi angle
Auteurs : Gurel, Basak (Auteur de la Conférence)
CIRM (Editeur )
53D40 - Floer homology and cohomology, symplectic aspects
37J11 - Symplectic and canonical mappings
37J46 - Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems
CIRM (Editeur )
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Résumé :
The spectral norm is an important invariant of a Hamiltonian diffeomorphism and its properties have recently found numerous nontrivial applications to dynamics. We will explore the behavior of the spectral norm under iterations of a Hamiltonian diffeomorphism and some related phenomena. This feature is closely related to the existence of invariant sets (the Le Calvez–Yoccoz type theorems), Hamiltonian pseudo-rotations, rigidity and the strong closing lemma. The talk is based on joint work with Erman Çineli and Viktor Ginzburg.
Keywords : topological entropy; periodic orbits; hamiltonian diffeomorphisms; floer homology; persistence homology and barcodes
Codes MSC : Keywords : topological entropy; periodic orbits; hamiltonian diffeomorphisms; floer homology; persistence homology and barcodes
53D40 - Floer homology and cohomology, symplectic aspects
37J11 - Symplectic and canonical mappings
37J46 - Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems
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Informations sur la Vidéo
Réalisateur : Petit, JeanLangue : Anglais Date de publication : 21/07/2023 Date de captation : 04/07/2023 Sous collection : Research talks arXiv category : Symplectic Geometry ; Dynamical Systems Domaine : Dynamical Systems & ODE ; Geometry ; Topology Format : MP4 (.mp4) - HD Durée : 01:07:44 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/Carmin\2023-07-04_Gurel_1.mp4 
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Informations sur la Rencontre
Nom de la rencontre : From smooth to $C^{0}$ symplectic geometry: topological aspects and dynamical implications / Géométrie symplectique de lisse à $C^{0}$: aspects topologiques et implications dynamiquesOrganisateurs de la rencontre : Benedetti, Gabriele ; Humilière, Vincent ; Leclercq, Rémi ; Sandon, Sheila ; Seyfaddini, Sobhan Dates : 03/07/2023 - 07/07/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2759.html
Données de citation
DOI : 10.24350/CIRM.V.20068403Citer cette vidéo: Gurel, Basak (2023). The spectral norm, rigidity and all that. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20068403 URI : http://dx.doi.org/10.24350/CIRM.V.20068403 |
Voir aussi
- [Multi angle] The Humilière completion and some applications / Auteur de la Conférence Viterbo, Claude.
- [Multi angle] Contact topology and thermodynamics / Auteur de la Conférence Polterovich, Leonid.
- [Multi angle] Symplectic mapping class groups: structural properties from smooth to $C^{0}$ / Auteur de la Conférence Keating, Ailsa.
- [Multi angle] Symplectic capacities of domains close to the ball and quasi-invariant contact forms / Auteur de la Conférence Abbondandolo, Alberto.
Bibliographie
- Cineli, Erman, Viktor L. Ginzburg, and Basak Z. Gurel. "On the growth of the Floer barcode." arXiv preprint arXiv:2207.03613 (2022). - https://doi.org/10.48550/arXiv.2207.03613
- Аносов, Дмитрий Викторович, and Анатолий Борисович Каток. "Новые примеры в гладкой эргодической теории. Эргодические диффеоморфизмы." Труды Московского математического общества 23.0 (1970): 3-36. - https://www.mathnet.ru/eng/mmo237
- Cineli, Erman, Viktor L. Ginzburg, and Basak Z. Gurel. "Topological entropy of Hamiltonian diffeomorphisms: a persistence homology and Floer theory perspective." arXiv preprint arXiv:2111.03983 (2021). - https://doi.org/10.48550/arXiv.2111.03983
- Ginzburg, Viktor L., and Başak Z. Gürel. "Hamiltonian pseudo-rotations of projective spaces." Inventiones mathematicae 214.3 (2018): 1081-1130. - http://dx.doi.org/10.1007/s00222-018-0818-9
- Ginzburg, Viktor L., and Başak Z. Gürel. "Approximate identities and Lagrangian Poincaré recurrence." Arnold Mathematical Journal 5.1 (2019): 5-14. - http://dx.doi.org/10.1007/s40598-019-00097-9
- Kislev, Asaf, and Egor Shelukhin. "Bounds on spectral norms and barcodes." Geometry & Topology 25.7 (2022): 3257-3350. - https://doi.org/10.2140/gt.2021.25.3257
- Le Roux, Frédéric, and Sobhan Seyfaddini. "The Anosov–Katok method and pseudo-rotations in symplectic dynamics." Journal of Fixed Point Theory and Applications 24.2 (2022): 36. - http://dx.doi.org/10.1007/s11784-022-00955-8
- Usher, Michael, and Jun Zhang. "Persistent homology and Floer–Novikov theory." Geometry & Topology 20.6 (2016): 3333-3430. - https://doi.org/10.2140/gt.2016.20.3333
- Viterbo, Claude. "Symplectic topology as the geometry of generating functions." Mathematische Annalen 292.1 (1992): 685-710. - http://eudml.org/doc/164936
