Systems of Transversal Sections near Critical Energy Levels of Hamiltonian Systems in ℝ⁴

DOI10.1090/memo/1202zbMath1486.53099arXiv1310.8464OpenAlexW2790754227MaRDI QIDQ4645819

Pedro A. S. Salomão, Naiara V. de Paulo

Publication date: 11 January 2019

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.8464

zbMATH Keywords

periodic orbitshomoclinic orbitsHamiltonian dynamicspseudo-holomorphic curvessystems of transversal sections

Mathematics Subject Classification ID

Global theory of symplectic and contact manifolds (53D35) Contact systems (37J55) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

Related Items (8)

Elliptic bindings for dynamically convex Reeb flows on the real projective three-space ⋮ On the existence of connecting orbits for critical values of the energy ⋮ Genus zero global surfaces of section for Reeb flows and a result of Birkhoff ⋮ On the existence of supporting broken book decompositions for contact forms in dimension 3 ⋮ Global diffusion on a tight three-sphere ⋮ Global surfaces of section for dynamically convex Reeb flows on lens spaces ⋮ On the multiplicity of periodic orbits and homoclinics near critical energy levels of Hamiltonian systems in $\mathbb {R}^4$ ⋮ Reeb flows, pseudo-holomorphic curves and transverse foliations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
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• Elliptic bindings for dynamically convex Reeb flows on the real projective three-space
• Dynamical aspects of multi-round horseshoe-shaped homoclinic orbits in the RTBP
• On the existence of disk-like global sections for Reeb flows on the tight 3-sphere
• Intersection theory of punctured pseudoholomorphic curves
• Connected sums and finite energy foliations. I: Contact connected sums
• Global surfaces of section in non-regular convex energy levels of Hamiltonian systems
• The local behaviour of holomorphic curves in almost complex 4-manifolds
• Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center
• Contact 3-manifolds twenty years since J. Martinet's work
• The dynamics on three-dimensional strictly convex energy surfaces
• Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three
• Finite energy foliations of tight three-spheres and Hamiltonian dynamics
• Homoclinic orbit to a center manifold
• Conservative dynamics: unstable sets for saddle-center loops.
• Compactness results in symplectic field theory
• Homoclinic orbits in families of hypersurfaces with hyperbolic periodic orbits
• Strictly convex submanifolds and hypersurfaces of positive curvature.
• Convex energy levels of Hamiltonian systems
• Properties of pseudoholomorphic curves in symplectisations. I: Asymptotics
• Existence of homoclinic solutions to periodic orbits in a center manifold
• Properties of pseudo-holomorphic curves in symplectisations. II: Embedding controls and algebraic invariants
• A characterisation of the tight three-sphere
• A Poincaré-Birkhoff theorem for tight Reeb flows on \(S^3\)
• Systems of global surfaces of section for dynamically convex Reeb flows on the 3-sphere
• On the ultimate behavior of orbits with respect to an unstable critical point. I: Oscillating, asymptotic, and capture orbits
• The Conley-Zehnder index and the saddle-center equilibrium
• Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung
• A dynamical characterization of universally tight lens spaces
• Contact geometry of the restricted three-body problem
• On the generalization of a theorem of A. Liapounoff
• Relative asymptotic behavior of pseudoholomorphic half-cylinders
• A characterization of the tight 3-sphere II
• On normal forms in Hamiltonian dynamics, a new approach to some convergence questions
• Irregular dynamics and homoclinic orbits to Hamiltonian saddle centers
• PERIODIC AND HOMOCLINIC ORBITS IN A TWO-PARAMETER UNFOLDING OF A HAMILTONIAN SYSTEM WITH A HOMOCLINIC ORBIT TO A SADDLE-CENTER
• Global properties of tight Reeb flows with applications to Finsler geodesic flows on S²
• Fast finite-energy planes in symplectizations and applications
• Low Energy Transit Orbits in the Restricted Three-Body Problems
• Multibump solutions homoclinic to periodic orbits of large energy in a centre manifold

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