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

    Armands Gritsans   Affiliation
    ; Inara Yermachenko   Affiliation

Abstract

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.

Keyword : conservative equation, Morse function, period annulus, binary tree

How to Cite
Gritsans, A., & Yermachenko, I. (2021). On the maximum number of period annuli for second order conservative equations. Mathematical Modelling and Analysis, 26(4), 612-630. https://doi.org/10.3846/mma.2021.13979
Published in Issue
Nov 26, 2021
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