Cone structures from a dynamical and probabilistic viewpoint

TL;DR

This paper investigates the geometric and probabilistic dynamics of cone structures related to open book decompositions, inspired by the circular restricted three body problem, revealing obstructions in phase space navigation.

Contribution

It introduces a novel geometric and probabilistic framework for analyzing cone structures in dynamical systems, particularly in the context of the CR3BP.

Findings

Identifies geometric obstructions in phase space navigation.

Connects cone structures to open book decompositions.

Provides insights into the dynamics of the CR3BP.

Abstract

The goal of this note is to explore, from a geometric and probabilistic point of view, the dynamics of cone structures adapted to open book decompositions. This is inspired by the picture which arises in the study of the circular restricted three body problem (CR3BP). This yields geometric obstructions to reaching a point from another point in the phase space of the CR3BP.