---
author:
- 'J. Slíz [^1], T. Kovács'
- 'Á. Süli'
title: Chaos Control with Ion Propulsion
---

Introduction
============

Finite time chaotic behaviour is a common phenomenon in simple as well as in complex dynamical systems. Transient chaos in Hamiltonian dynamics appears as chaotic scattering (Bleher, Grebogi & Ott 1990) or half-scattering. This can later be thought as of escape or capture from or into a system. The finite time chaotic motion might proceed before the particle leaves the systems, say interacting with a scatter object, after which the irregular motion might cease.

Escape in simple dynamical systems has been extensively studied for roughly 25 years, [*for more details Ott (1993), Gaspard (1998), Contopulos (2004), Lai & Tél (2011)*]{}. Theory of transient chaos states that finite time chaotic behaviour is related to the unstable periodic orbits and their stable and unstable manifolds in the phase space. In addition, one can construct numerically a well-defined fractal set in the phase space containing all the heteroclinic and homoclinic intersections of these manifolds as well as the unstable periodic orbits themselves. This fractal set is responsible for finite time chaotic behaviour. Some textbooks call this set the chaotic saddle, indicating its non-attracting 