二阶保守方程的最大周期环数

IF 1.6 3区数学 Q1 MATHEMATICS

Mathematical Modelling and Analysis Pub Date : 2021-11-26 DOI:10.3846/mma.2021.13979

A. Gritsans, Inara Yermachenko

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引用次数: 1

摘要

考虑一类二阶标量保守微分方程，其势函数为具有有限个临界点的莫尔斯函数，且在无穷远处无界。给出了该方程的非全局非平凡周期环数的上界，并证明了所得到的上界是尖锐的。我们在考虑时使用树形理论。

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On the Maximum number of period annuli for second order conservative equations

We consider a second order scalar conservative differential equation whose potential function is a Morse function with a finite number of critical points and is unbounded at infinity. We give an upper bound for the number of nonglobal nontrivial period annuli of the equation and prove that the upper bound obtained is sharp. We use tree theory in our considerations.

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