Local control of area-preserving maps

TL;DR

This paper introduces a method to control chaos in area-preserving maps by adding a small, explicit control term that preserves the map's area and creates a known invariant curve.

Contribution

The paper provides an explicit control term for area-preserving maps, enabling chaos control while maintaining the map's area-preserving property.

Findings

Controlled map retains area-preserving property

Invariant curve with known equation is created

Control term is explicitly derived

Abstract

We present a method of control of chaos in area-preserving maps. This method gives an explicit expression of a control term which is added to a given area-preserving map. The resulting controlled map which is a small and suitable modification of the original map, is again area-preserving and has an invariant curve whose equation is explicitly known.