In this paper,we establish a relationship between the Morse index at rest points in the saddle point reduction and the brake-orbit-type Maslov index at corresponding brake orbits.As an application,we give a criterion ...In this paper,we establish a relationship between the Morse index at rest points in the saddle point reduction and the brake-orbit-type Maslov index at corresponding brake orbits.As an application,we give a criterion to find brake orbits which are contractible and start at{0}×T^n■T^2n for even Hamiltonian on T^2 n by the methods of the Maslov-index theory and a critical point theorem formulated by Bartsch and Wang(1997).Explicitly,if all trivial solutions of a Hamiltonian are nondegenerate in the brake orbit boundary case,there are at least max{iL0(z0)}pairs of nontrivial 1-periodic brake orbits if iL0(z0)>0 or at least max{-iL0(z0)-n}pairs of nontrivial 1-periodic brake orbits if iL0(z0)<-n.In the end,we give an example to find brake orbits for certain Hamiltonian via this criterion.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11790271,11771341 and 11422103)and Nankai University。
文摘In this paper,we establish a relationship between the Morse index at rest points in the saddle point reduction and the brake-orbit-type Maslov index at corresponding brake orbits.As an application,we give a criterion to find brake orbits which are contractible and start at{0}×T^n■T^2n for even Hamiltonian on T^2 n by the methods of the Maslov-index theory and a critical point theorem formulated by Bartsch and Wang(1997).Explicitly,if all trivial solutions of a Hamiltonian are nondegenerate in the brake orbit boundary case,there are at least max{iL0(z0)}pairs of nontrivial 1-periodic brake orbits if iL0(z0)>0 or at least max{-iL0(z0)-n}pairs of nontrivial 1-periodic brake orbits if iL0(z0)<-n.In the end,we give an example to find brake orbits for certain Hamiltonian via this criterion.
