Dynamical convexity and closed orbits on symmetric spheres

DOI10.1215/00127094-2020-0097zbMath1477.37068arXiv1912.04882OpenAlexW3153185293MaRDI QIDQ2037856

Leonardo Macarini, Viktor L. Ginzburg

Publication date: 8 July 2021

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.04882

zbMATH Keywords

contact formclosed Reeb orbitsReeb flowsdynamical convexityantipodal symmetryConley-Zenhnder index

Mathematics Subject Classification ID

Contact manifolds (general theory) (53D10) Symplectic aspects of Floer homology and cohomology (53D40) Index theory for dynamical systems, Morse-Conley indices (37B30) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Contact systems (37J55) Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods (37J51) Symplectic and canonical mappings (37J11)

Related Items (4)

Dynamical implications of convexity beyond dynamical convexity ⋮ 3D convex contact forms and the Ruelle invariant ⋮ Generalized common index jump theorem with applications to closed characteristics on star-shaped hypersurfaces and beyond ⋮ Multiplicity of closed geodesics on bumpy Finsler manifolds with elliptic closed geodesics

Cites Work

• Unnamed Item
• 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 Reeb orbits on the sphere and symplectically degenerate maxima
• 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
• Multiplicity of closed characteristics on symmetric convex hypersurfaces in \(\mathbb{R}^{2n}\)
• The dynamics on three-dimensional strictly convex energy surfaces
• Bott formula of the Maslov-type index theory
• Closed characteristics on compact convex hypersurfaces in \(\mathbb{R}^{2n}\)
• Multiplicity of closed Reeb orbits on prequantization bundles
• Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in \(\mathbb{R}^{2n}\)
• Index theory for symplectic paths with applications
• Maslov-type index theory for symplectic paths and spectral flow. II
• Maslov-type index theory for symplectic paths and spectral flow. I
• Lusternik-Schnirelmann theory and closed Reeb orbits
• Multiplicity and ellipticity of closed characteristics on compact star-shaped hypersurfaces in \(\mathbb R^{2n}\)
• Spectral asymmetry and Riemannian Geometry. I
• The Spectral Flow and the Maslov Index
• Local contact homology and applications
• From one Reeb orbit to two

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