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

Abdellah Menasri

Higher National School of Forests, Khenchela, Algeria

Email address: abdellah.menasri70@gmail.com

Doi : https://doi.org/10.47013/15.4.25

Cited by : Jordan J. Math & Stat., 15 (4B) (2022), 1173 - 1192

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Received on: Dec. 19, 2021;                                           Accepted on: May 11, 2022

 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.

Keywords: Stable and Unstable Manifolds, Two-Dimensional, Piecewise-Linear Normal Form Maps.