We consider Hamiltonian functions of the classical type, namely, even and convex with respect to the generalized momenta. A brake orbit is a periodic solution of Hamilton’s equations such that the generalized momenta are zero on two different points. Under mild assumptions, this paper reduces the multiplicity problem of the brake orbits for a Hamiltonian function of the classical type to the multiplicity problem of orthogonal geodesic chords in a concave Finslerian manifold with boundary. This paper will be used for a generalization of a Seifert’s conjecture about the multiplicity of brake orbits to Hamiltonian functions of the classical type.

中文翻译：

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通过奇异 Finsler 度量中的测地线对经典类型哈密顿系统的制动轨道

我们考虑经典类型的哈密顿函数，即关于广义动量的偶数和凸函数。制动轨道是汉密尔顿方程组的周期解，使得广义动量在两个不同点上为零。在温和的假设下，本文将经典类型哈密顿函数的制动轨道多重性问题简化为带边界的凹芬斯勒流形中正交测地弦的多重性问题。本文将用于将 Seifert 的关于制动轨道多重性的猜想推广到经典类型的哈密顿函数。