Minimal Period Estimates for Brake Orbits of Nonlinear Symmetric Hamiltonian Systems

Infinite dimensional hamiltonian systems and nonlinear wave equation: periodic orbits with long minimal period

Numerical Continuation of Hamiltonian Relative Periodic Orbits

The bifurcation theory and numerics of periodic orbits of general dynamical systems is well developed, and in recent years there has been rapid progress in the development of a bifurcation theory for dynamical systems with structure, such as symmetry or symplecticity. But as yet there are few results on the numerical computation of those bifurcations. The methods we present in this paper are a ...

Iteration theory of Maslov-type index associated with a Lagrangian subspace for symplectic paths and Multiplicity of brake orbits in bounded convex symmetric domains

In this paper, we first establish the Bott-type iteration formulas and some abstract precise iteration formulas of the Maslov-type index theory associated with a Lagrangian subspace for symplectic paths. As an application, we prove that there exist at least [ n 2 ] + 1 geometrically distinct brake orbits on every C compact convex symmetric hypersurface Σ in R satisfying the reversible condition...

Analytical Mini-Max Methods for Hamiltonian Brake Orbits of Prescribed Energy

More specifically, we shall look for brake orbits (cf. [ 19]), i.e., nonconstant solutions of (1.1) which satisfy for some T > 0 Q(O) = 4(T) = 0. (1.2) Upon periodic continuation, a solution of (1.1 ), (1.2) will produce a periodic solution of (1.1) with period 2T. The trajectory in configuration space of such a motion is a simple curve connecting the two “restpoints” q(0) and q(T) along which ...

Existence of Relative Periodic Orbits near Relative Equilibria

We show existence of relative periodic orbits (a.k.a. relative nonlinear normal modes) near relative equilibria of a symmetric Hamiltonian system under an appropriate assumption on the Hessian of the Hamiltonian. This gives a relative version of the Moser-Weinstein theorem.