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Lusternik-Schnirelmann theory and closed Reeb orbits (Q2182425)

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English	Lusternik-Schnirelmann theory and closed Reeb orbits	scientific article

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scholarly article

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Lusternik-Schnirelmann theory and closed Reeb orbits (English)

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Viktor L. Ginzburg

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Başak Z. Gürel

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Mathematische Zeitschrift

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publication date

23 May 2020

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full work available at URL

https://arxiv.org/abs/1601.03092

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zbMATH Keywords

periodic orbits

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Reeb flows

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Floer and symplectic homology

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Lusternik-Schnirelmann theory

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Conley-Zehnder index

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MaRDI profile type

MaRDI publication profile

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Floer homology of cotangent bundles and the loop product

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Dynamical convexity and elliptic periodic orbits for Reeb flows

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Multiplicity of periodic orbits for dynamically convex contact forms

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Periodic Reeb orbits on prequantization bundles

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On a theorem by Ekeland and Lasry concerning the number of periodic Hamiltonian trajectories

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Dynamical systems. IV. Symplectic geometry and its applications. Transl. from the Russian by G. Wassermann.

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Existence d'orbites périodiques complètement elliptiques des Hamiltoniens convexes présentant certaines symétries

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Existence of closed geodesics on positively curved manifolds

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The existence of two closed geodesics on every Finsler 2-sphere

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Euler and Maslov cocycles

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On the rigidity of the coisotropic Maslov index on certain rational symplectic manifolds

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Symplectic homology, autonomous Hamiltonians, and Morse-Bott moduli spaces

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Fredholm theory and transversality for the parametrized and for the \(S^{1}\)-invariant symplectic action

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The index of Floer moduli problems for parametrized action functionals

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THE GYSIN EXACT SEQUENCE FOR S<sup>1</sup>-EQUIVARIANT SYMPLECTIC HOMOLOGY

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<i>S</i><sup>1</sup>-Equivariant Symplectic Homology and Linearized Contact Homology

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Pseudo-rotations with sufficiently Liouvillean rotation number are \(C^0\)-rigid

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Action-index relations for perfect Hamiltonian diffeomorphisms

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Rabinowitz Floer homology and symplectic homology

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Reeb vector fields and open book decompositions

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From one Reeb orbit to two

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Closed curves on convex hypersurfaces and periods of nonlinear oscillations

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The enhanced common index jump theorem for symplectic paths and non-hyperbolic closed geodesics on Finsler manifolds

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Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in \(\mathbb{R}^{2n}\)

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Convex Hamiltonian energy surfaces and their periodic trajectories

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Symplectic topology and Hamiltonian dynamics

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On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface

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On the mean Euler characteristic of contact manifolds

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Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems

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Cuplength estimates on lagrangian intersections

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Symplectic fixed points and holomorphic spheres

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Coisotropic intersections

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The Conley conjecture

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Iterated index and the mean Euler characteristic

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Action and index spectra and periodic orbits in Hamiltonian dynamics

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On the generic existence of periodic orbits in Hamiltonian dynamics

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Periodic orbits of twisted geodesic flows and the Weinstein-Moser theorem

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Local Floer homology and the action gap

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Hyperbolic fixed points and periodic orbits of Hamiltonian diffeomorphisms

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The Conley conjecture and beyond

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On the Conley conjecture for Reeb flows

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Multiplicity of closed Reeb orbits on prequantization bundles

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Closed Reeb orbits on the sphere and symplectically degenerate maxima

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Homological Resonances for Hamiltonian Diffeomorphisms and Reeb Flows

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On the filtered symplectic homology of prequantization bundles

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Loop products and closed geodesics

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Shortening embedded curves

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Periodic geodesics on compact Riemannian manifolds

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On non-contractible periodic orbits of Hamiltonian diffeomorphisms

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Perfect Reeb flows and action-index relations

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Generalized Conley-Zehnder index

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The positive equivariant symplectic homology as an invariant for some contact manifolds

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Symplectic capacities from positive \(S^1\)-equivariant symplectic homology

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On the minimal number of periodic orbits on some hypersurfaces in \(\mathbb{R}^{2n}\)

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Dynamically convex Finsler metrics and \(J\)-holomorphic embedding of asymptotic cylinders

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Lusternik-Schnirelman-theory for Lagrangian intersections

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The dynamics on three-dimensional strictly convex energy surfaces

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Local contact homology and applications

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ERGODIC PERTURBATIONS OF DEGENERATE INTEGRABLE HAMILTONIAN SYSTEMS

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Rigid constellations of closed Reeb orbits

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Brieskorn manifolds in contact topology

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A module structure on the symplectic Floer cohomology

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The existence of two closed characteristics on every compact star-shaped hypersurface in \(\mathbb{R}^{4}\)

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Multiplicity of closed characteristics on symmetric convex hypersurfaces in \(\mathbb{R}^{2n}\)

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Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems

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A Maslov-type index theory for symplectic paths

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Index theory for symplectic paths with applications

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Resonance identities for closed characteristics on compact star-shaped hypersurfaces in \(\mathbf R^{2n}\)

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Closed characteristics on compact convex hypersurfaces in \(\mathbb{R}^{2n}\)

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Local Floer homology and infinitely many simple Reeb orbits

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On a generic property of geodesic flows

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A sphere theorem for non-reversible Finsler metrics

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Topological quantum field theory structure on symplectic cohomology

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The Maslov index for paths

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Morse Theory, the Conley Index and Floer Homology

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Morse theory for periodic solutions of hamiltonian systems and the maslov index

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A quantum cup-length estimate for symplectic fixed points

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Equivariant Morse Theory for Starshaped Hamiltonian Systems

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Some remarks on Massey products, tied cohomology classes, and the Lusternik-Shnirelman category

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Functors and computations in Floer homology with applications. I

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On a conjecture of Anosov

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Closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{8}\)

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Existence of closed characteristics on compact convex hypersurfaces in \(\mathbf{R}^{2n}\)

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Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces

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Spectral numbers in Floer theories

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Geometry of the Katok examples

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Identifiers

zbMATH Open document ID

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10.1007/s00209-019-02361-2

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2182425

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