On the Lyapunov exponent spectrum
by
Vladimir A. Dobrynskiy
Institute for Metal Physics of National Academy of Sciences of Ukraine, 36 Academician Vernadsky Blvd., 03680 Kiev-142 UKRAINE

AMS Subject Classification: 34D05 + 58F99 (asymptotic properties; characteristic exponents + dynamical systems);

A fixed (periodic) point of map is asymptotic stable iff all its the Lyapunov exponents evaluated at the given point are negative. Transition of one of the exponents through zero generates a bifurcation of phase pattern in the given point neighbourhood. There is a hypothesis that an asymptotic stability and bifurcation of non-trivial topologically transitive subsets of map are connected with negativity of the Lyapunov exponents evaluated at all the subset points. The latter is a reason to study the Lyapunov exponent spectrum. We have the following rigorous mathematical results: (1) the most of piece-wise linear maps have continuous the Lyapunov exponent spectrum, (2) that of the logistic map is countable at the least.

Date received: October 2, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calu-13.