Autonomous Hamiltonian flows, Hofer's geometry and persistence modules

DOI10.1007/s00029-015-0201-2zbMath1337.53094arXiv1412.8277OpenAlexW2963936239MaRDI QIDQ907070

Egor Shelukhin, Leonid Polterovich

Publication date: 1 February 2016

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.8277

zbMATH Keywords

symplectic manifoldHamiltonian flowFloer theorypersistence modulesloop rotations operators

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Hamilton's equations (70H05) Dynamics induced by flows and semiflows (37C10) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (43)

Legendrian persistence modules and dynamics ⋮ Symplectic rigidity and quantum mechanics ⋮ Families of legendrians and Lagrangians with unbounded spectral norm ⋮ On the Hofer–Zehnder conjecture on ℂPd via generating functions ⋮ Quantitative Heegaard Floer cohomology and the Calabi invariant ⋮ The fiber of persistent homology for simplicial complexes ⋮ Symplectic Banach–Mazur distances between subsets of ℂn ⋮ A \(C^0\) counterexample to the Arnold conjecture ⋮ Another look at the Hofer-Zehnder conjecture ⋮ On the Hofer-Zehnder conjecture ⋮ Viterbo conjecture for Zoll symmetric spaces ⋮ Relative growth rate and contact Banach-Mazur distance ⋮ Lagrangian configurations and Hamiltonian maps ⋮ Hofer's metric in compact Lie groups ⋮ Hofer's geometry and topological entropy ⋮ On the autonomous norm on the group of Hamiltonian diffeomorphisms of the torus ⋮ Symplectic cohomology and a conjecture of Viterbo ⋮ Remarks on the oscillation energy of Legendrian isotopies ⋮ Hamiltonian no-torsion ⋮ Fukaya A ∞-structures Associated to Lefschetz Fibrations. II ⋮ Random chain complexes ⋮ A quasi-isometric embedding into the group of Hamiltonian diffeomorphisms with Hofer's metric ⋮ Continuous flows generate few homeomorphisms ⋮ On the iterated Hamiltonian Floer homology ⋮ The Conley conjecture and beyond ⋮ Symplectic homology and the Eilenberg-Steenrod axioms ⋮ The persistence of the Chekanov-Eliashberg algebra ⋮ Non-contractible Periodic Orbits in Hamiltonian Dynamics on Closed Symplectic Manifolds ⋮ The action spectrum and \(C^0\) symplectic topology ⋮ Entropy and quasimorphisms ⋮ On the filtered symplectic homology of prequantization bundles ⋮ Non-autonomous curves on surfaces ⋮ Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms ⋮ Applications of square roots of diffeomorphisms ⋮ Barcodes and area-preserving homeomorphisms ⋮ A brief survey of the spectral numbers in floer homology ⋮ Bounds on the Lagrangian spectral metric in cotangent bundles ⋮ Bounds on spectral norms and barcodes ⋮ Spectral spread and non-autonomous Hamiltonian diffeomorphisms ⋮ Persistence modules, symplectic Banach–Mazur distance and Riemannian metrics ⋮ Dynamically exotic contact spheres in dimensions \(\geq 7\) ⋮ A relative Hofer estimate and the asymptotic Hofer-Lipschitz constant ⋮ On the Hofer–Zehnder conjecture on weighted projective spaces

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