Lusternik-Schnirelmann theory and closed Reeb orbits

DOI10.1007/s00209-019-02361-2zbMath1440.53100arXiv1601.03092OpenAlexW2965262309MaRDI QIDQ2182425

Başak Z. Gürel, Viktor L. Ginzburg

Publication date: 23 May 2020

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.03092

zbMATH Keywords

periodic orbitsConley-Zehnder indexReeb flowsLusternik-Schnirelmann theoryFloer and symplectic homology

Mathematics Subject Classification ID

Symplectic aspects of Floer homology and cohomology (53D40) Contact systems (37J55) Symplectic and canonical mappings (37J11)

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Cites Work

• Unnamed Item
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• The existence of two closed characteristics on every compact star-shaped hypersurface in \(\mathbb{R}^{4}\)
• Existence of closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{2n}\)
• Closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{8}\)
• Closed Reeb orbits on the sphere and symplectically degenerate maxima
• Action-index relations for perfect Hamiltonian diffeomorphisms
• On a conjecture of Anosov
• Generalized Conley-Zehnder index
• The Conley conjecture and beyond
• On the minimal number of periodic orbits on some hypersurfaces in \(\mathbb{R}^{2n}\)
• The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds
• Multiplicity of periodic orbits for dynamically convex contact forms
• The Conley conjecture
• Some remarks on Massey products, tied cohomology classes, and the Lusternik-Shnirelman category
• Local Floer homology and infinitely many simple Reeb orbits
• Multiplicity of closed characteristics on symmetric convex hypersurfaces in \(\mathbb{R}^{2n}\)
• Local Floer homology and the action gap
• Action and index spectra and periodic orbits in Hamiltonian dynamics
• Periodic orbits of twisted geodesic flows and the Weinstein-Moser theorem
• Dynamically convex Finsler metrics and \(J\)-holomorphic embedding of asymptotic cylinders
• On the generic existence of periodic orbits in Hamiltonian dynamics
• Floer homology of cotangent bundles and the loop product
• Fredholm theory and transversality for the parametrized and for the \(S^{1}\)-invariant symplectic action
• Loop products and closed geodesics
• Existence of closed geodesics on positively curved manifolds
• Symplectic topology and Hamiltonian dynamics
• Convex Hamiltonian energy surfaces and their periodic trajectories
• Lusternik-Schnirelman-theory for Lagrangian intersections
• On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface
• Closed curves on convex hypersurfaces and periods of nonlinear oscillations
• On a theorem by Ekeland and Lasry concerning the number of periodic Hamiltonian trajectories
• Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems
• Euler and Maslov cocycles
• Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems
• Shortening embedded curves
• A quantum cup-length estimate for symplectic fixed points
• The dynamics on three-dimensional strictly convex energy surfaces
• On a generic property of geodesic flows
• The Maslov index for paths
• A Maslov-type index theory for symplectic paths
• A sphere theorem for non-reversible Finsler metrics
• A module structure on the symplectic Floer cohomology
• Closed characteristics on compact convex hypersurfaces in \(\mathbb{R}^{2n}\)
• Multiplicity of closed Reeb orbits on prequantization bundles
• Symplectic capacities from positive \(S^1\)-equivariant symplectic homology
• Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in \(\mathbb{R}^{2n}\)
• The positive equivariant symplectic homology as an invariant for some contact manifolds
• Periodic Reeb orbits on prequantization bundles
• Symplectic fixed points and holomorphic spheres
• Index theory for symplectic paths with applications
• Reeb vector fields and open book decompositions
• Functors and computations in Floer homology with applications. I
• Perfect Reeb flows and action-index relations
• Pseudo-rotations with sufficiently Liouvillean rotation number are \(C^0\)-rigid
• Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces
• The index of Floer moduli problems for parametrized action functionals
• On the rigidity of the coisotropic Maslov index on certain rational symplectic manifolds
• Dynamical convexity and elliptic periodic orbits for Reeb flows
• Hyperbolic fixed points and periodic orbits of Hamiltonian diffeomorphisms
• Coisotropic intersections
• Resonance identities for closed characteristics on compact star-shaped hypersurfaces in \(\mathbf R^{2n}\)
• Symplectic homology, autonomous Hamiltonians, and Morse-Bott moduli spaces
• Periodic geodesics on compact Riemannian manifolds
• The existence of two closed geodesics on every Finsler 2-sphere
• Brieskorn manifolds in contact topology
• On non-contractible periodic orbits of Hamiltonian diffeomorphisms
• THE GYSIN EXACT SEQUENCE FOR S¹-EQUIVARIANT SYMPLECTIC HOMOLOGY
• On the mean Euler characteristic of contact manifolds
• Rabinowitz Floer homology and symplectic homology
• Homological Resonances for Hamiltonian Diffeomorphisms and Reeb Flows
• Morse Theory, the Conley Index and Floer Homology
• Spectral numbers in Floer theories
• Equivariant Morse Theory for Starshaped Hamiltonian Systems
• Morse theory for periodic solutions of hamiltonian systems and the maslov index
• ERGODIC PERTURBATIONS OF DEGENERATE INTEGRABLE HAMILTONIAN SYSTEMS
• Existence d'orbites périodiques complètement elliptiques des Hamiltoniens convexes présentant certaines symétries
• Rigid constellations of closed Reeb orbits
• S¹-Equivariant Symplectic Homology and Linearized Contact Homology
• Cuplength estimates on lagrangian intersections
• On the filtered symplectic homology of prequantization bundles
• Geometry of the Katok examples
• Local contact homology and applications
• Iterated index and the mean Euler characteristic
• On the Conley conjecture for Reeb flows
• Topological quantum field theory structure on symplectic cohomology
• Dynamical systems. IV. Symplectic geometry and its applications. Transl. from the Russian by G. Wassermann.
• From one Reeb orbit to two