An index theory and existence of multiple brake orbits for star-shaped Hamiltonian systems
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Publication:1101752
DOI10.1007/BF01446433zbMath0642.58030MaRDI QIDQ1101752
Publication date: 1989
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/164506
periodic solutionscritical pointsHamiltonian systemmultiple critical pointsrelative indexbrake orbits
Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Local and nonlocal bifurcation theory for dynamical systems (37G99)
Related Items (28)
Periodic orbits of Hamiltonian systems on symmetric positive-type hypersurfaces ⋮ Minimal brake orbits of first-order convex Hamiltonian systems with anisotropic growth ⋮ Brake orbits for Hamiltonian systems of the classical type via geodesics in singular Finsler metrics ⋮ Brake subharmonic solutions of subquadratic Hamiltonian systems ⋮ Seifert Conjecture in the Even Convex Case ⋮ Some progress on minimal period problems in reversible semi-positive Hamiltonian systems ⋮ A note on the existence of multiple brake orbits ⋮ The brake orbits of Hamiltonian systems on positive-type hypersurfaces ⋮ Equivariant wrapped Floer homology and symmetric periodic Reeb orbits ⋮ Higher \(P\)-symmetric Ekeland-Hofer capacities ⋮ Multiple solutions for a class of generalized critical noncooperative Schrödinger systems in \(\mathbb{R}^N\) ⋮ Multiple subharmonic solutions in Hamiltonian system with symmetries ⋮ Brake subharmonic solutions of first order Hamiltonian systems ⋮ A limit index theory and its applications ⋮ Unnamed Item ⋮ Iteration theory of \(L\)-index and multiplicity of brake orbits ⋮ Minimal periodic problem for brake orbits of first-order Hamiltonian systems ⋮ Stability of the brake orbits on reversible symmetric compact convex hypersurfaces in \(R^{2n}\) ⋮ Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the \(N\)-dimensional disk ⋮ Multiple brake orbits in bounded convex symmetric domains ⋮ Multiple brake orbits on convex hypersurfaces under asymmetric pinch conditions ⋮ Index iteration theory for symplectic paths and multiple periodic solution orbits ⋮ Multiplicity of closed characteristics on \(P\)-symmetric compact convex hypersurfaces in \(\mathbb{R}^{2n}\) ⋮ Brake orbits of first order convex Hamiltonian systems with particular anisotropic growth ⋮ Multiple brake orbits on compact convex symmetric reversible hypersurfaces in \(\mathbb{R}^{2 n}\) ⋮ The study of minimal period estimates for brake orbits of autonomous subquadratic Hamiltonian systems ⋮ Brake orbits of super-quadratic Hamiltonian systems ⋮ The compact category and multiple periodic solutions of Hamiltonian systems on symmetric starshaped energy surfaces
Cites Work
- Multiple orbits for Hamiltonian systems on starshaped surfaces with symmetries
- A proof of Weinstein's conjecture in \(\mathbb R^{2n}\)
- Periodic solutions on hypersurfaces and a result by C. Viterbo
- On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface
- Periodic orbits for convex hamiltonian systems
- A \(Z_ p\)-Borsuk-Ulam theorem
- Periodische Bewegungen mechanischer Systeme
- Existence of multiple periodic orbits on star‐shaped hamiltonian surfaces
- Solutions of minimal period for a class of nonconvex Hamiltonian systems and applications to the fixed energy problem
- A p Borsuk-Ulam theorem and index theory with a multiplicity result in partial differential equations
- On Critical Point Theory for Indefinite Functionals in The Presence of Symmetries
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