Stable and Unstable Manifolds of the Two-Dimensional Piecewise-Linear Normal Form Maps

Abstract

The stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the idea of an attractor. In this paper, we will determine the stable and unstable manifolds of the normal form of two-dimensional piecewise-linear maps in the neighborhood of a fixed point at the border using stable manifold theorem, this is an important result about the structure of the set of orbits approaching to a hyperbolic fixed point.

Key words and phrases. Stable and Unstable Manifolds, Two-Dimensional, Piecewise-Linear Normal Form Maps.

2020 Mathematics Subject Classification. 32Q26