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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
PDF
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.
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