Bifurcation of dividing surfaces constructed from a pitchfork bifurcation of periodic orbits in a symmetric potential energy surface with a post-transition-state bifurcation

TL;DR

This paper investigates how dividing surfaces in a symmetric potential energy system bifurcate due to a pitchfork bifurcation of periodic orbits, affecting the structure and extent of these surfaces across energy levels.

Contribution

It introduces a detailed analysis of dividing surface bifurcation caused by pitchfork bifurcations in a symmetric two-degree-of-freedom Hamiltonian system.

Findings

Bifurcation of dividing surfaces occurs at the pitchfork bifurcation point.

The structure and extent of the dividing surfaces vary with energy.

The study characterizes the range and limits of these surfaces as energy changes.

Abstract

In this work we analyze the bifurcation of dividing surfaces that occurs as a result of a pitchfork bifurcation of periodic orbits in a two degrees of freedom Hamiltonian System. The potential energy surface of the system that we consider has four critical points: two minima, a high energy saddle and a lower energy saddle separating two wells (minima). In this paper we study the structure, the range, and the minimum and maximum extent of the periodic orbit dividing surfaces of the family of periodic orbits of the lower saddle as a function of the total energy.