Periodic Solutions of Hamiltonian Systems and Related Topics

ISBN-13: 9789027725530 / Angielski / Twarda / 1987 / 284 str.

P. H. Rabinowitz; A. Ambrosetti; Ivar Ekeland

Opis

This volume contains the proceedings of a NATO Advanced Research Workshop on Periodic Solutions of Hamiltonian Systems held in II Ciocco, Italy on October 13-17, 1986. It also contains some papers that were an outgrowth of the meeting. On behalf of the members of the Organizing Committee, who are also the editors of these proceedings, I thank all those whose contributions made this volume possible and the NATO Science Committee for their generous financial support. Special thanks are due to Mrs. Sally Ross who typed all of the papers in her usual outstanding fashion. Paul H. Rabinowitz Madison, Wisconsin April 2, 1987 xi 1 PERIODIC SOLUTIONS OF SINGULAR DYNAMICAL SYSTEMS Antonio Ambrosetti Vittorio Coti Zelati Scuola Normale Superiore SISSA Piazza dei Cavalieri Strada Costiera 11 56100 Pisa, Italy 34014 Trieste, Italy ABSTRACT. The paper contains a discussion on some recent advances in the existence of periodic solutions of some second order dynamical systems with singular potentials. The aim of this paper is to discuss some recent advances in th.e existence of periodic solutions of some second order dynamical systems with singular potentials.

Spis treści

Periodic Solutions of Singular Dynamical Systems.- Pseudo-Orbits of Contact Forms.- Some Applications of the Morse-Conley Theory to the Study of Periodic Solutions of Second Order Conservative Systems.- A “Birkhoff-Lewis” Type Result for Nonautonomous Hamiltonian Systems.- A Remark on A Priori Bounds and Existence for Periodic Solutions of Hamiltonian Systems.- On a Class of Nonlinear Problems with Lack of Compactness.- An Old-Fashioned Method in the Calculus of Variations.- Optimization and Periodic Trajectories.- Periodic Solutions of Dynamical Systems with Newtonian Type Potentials.- Families of Periodic Solutions Near Equilibrium.- Viterbo’s Proof of Weinstein’s Conjecture in R2n.- Global and Local Invariants for Convex Energy Surfaces and Their Periodic Trajectories: A Survey.- Viterbo’s Index and the Morse Index for the Symplectic Action.- Some Problems on the Hamilton-Jacobi Equation.- Some Results on Periodic Solutions of Mountain Pass Type for Hamiltonian Systems.- Remarks on Periodic Solutions for Some Dynamical Systems with Singularities.- Cauchy-Riemann Equation in Lagrange Intersection Theory.- Modulus of Continuity for Peierls’s Barrier.- Chaotic Orbits in the Three Body Problem.- On the Construction of Invariant Curves and Mather Sets via a Regularized Variational Principle.- The Obstruction Method and Some Numerical Experiments Related to the Standard Map.- On a Theorem of Hofer and Zehnder.- The Value Function of a Modified Jacobi Functional.- Perturbations of Nondegenerate Periodic Orbits of Hamiltonian Systems.- Remarks on Periodic Solutions on Hypersurfaces.