Non--Hyperbolic Dynamics: a Family of Special Functions

Details Non--Hyperbolic Dynamics: a Family of Special Functions Non--Hyperbolic Dynamics: a Family of Special Functions

1996-07-06

arxiv.org/abs/chao-dyn/9607002v1

Mathematics

Functional Analysis

Latex, 10 pages, 3 figures (available upon request to the Authors), presented at the Summer School/Conference Let's Face Chaos

Scientific paper

In this paper we present some theorems for a class of non--hyperbolic fixed points on ${\bf R}^N$ and then analyze a family of functions $f_{\theta}$ on the plane which have a non--hyperbolic fixed point in the origin. The dynamical properties of the family near the fixed point, like the basin of attraction, are studied. Finally the limits of applicability of the characterization by the eigenvalues of the Jacobian are discussed.

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