Multiple Brake Orbits on the Cotangent Space of Torus

Abstract

In this paper, we study the multiplicity of brake orbits on certain symplectic manifold. We give a criterion to find brake orbits for even Hamiltonian on the cotangent space of $\mathbb{T}^{n}$ by the methods of the Maslov-index theory and a critical point theorem formulated by Bartsch and Wang in [1]. More specifically, if H is even and satisfies certain growth conditions, one can find more brake orbits on the cotangent space of $\mathbb{T}^{n}$.

Keywords

Brake orbit / Maslov-type index / torus / saddle point reduction / critical point theorem

References

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