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Appears in collection : From smooth to $C^{0}$ symplectic geometry: topological aspects and dynamical implications / Géométrie symplectique de lisse à $C^{0}$: aspects topologiques et implications dynamiques

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.

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Citation data

  • DOI 10.24350/CIRM.V.20068403
  • Cite this video Gurel, Basak (04/07/2023). The spectral norm, rigidity and all that. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20068403
  • URL https://dx.doi.org/10.24350/CIRM.V.20068403


  • 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

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