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

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.

Keywords

• conservative equation
• morse function
• period annulus
• binary tree