ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Spectrum of a Dynamical System and Applied Symbolic Dinamics


George Osipenko

Laboratory of Nonlinear Analysis and Mathematical Modelling
State Technical University
St.Petersburg, 195251, Russia


The paper introduces a constructive method for localization of the Morse spectrum of a dynamical system on a vector bundle. The Morse spectrum is a limit set of Lyapunov exponents of periodic pseudo-trajectories. The proposed method does not demand any preliminary information on a system. An induced dynamical system on the projective bundle is associated with a directed graph called Symbolic Image. The symbolic image can be considered as a finite discrete approximation of a dynamical system. Valuable information about the system may come from the analysis of a symbolic image. In particular, a neighborhood of the Morse spectrum can be found. A special sequence of symbolic images is considered to obtain a sequence of embedded neighborhoods which converges to the Morse spectrum.

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