[Authors]
Osipenko, G.S.; Romanovskii, I.V.; Ampilova, N.B.; Petrenko, E.I.

[Title]
On Morse spectrum calculation

[AMS Subj-class]
Primary: 37D45, Secondary: 37F15, 37M05

[Keywords]
Morse spectrum, Lyapunov exponent, symbolic image, simplex-method, 
homoclinic point, hyperbolicity.

[Abstract]
   Morse spectrum of a dynamical system is a limit set of Lyapunov exponents
of periodic pseudo-trajectories. A constructive method, based on symbolic 
image conception, is considered to localize the Morse spectrum.
The symbolic image of a dynamical system is a finite discrete approximation 
and constitutes a directed graph.
The localizing method is based on a construction of special sequence
of symbolic images and a search of closed paths having the wanted 
characteristics. The main difficulty is that the number of such paths 
dramatically increases. A new simplex-method based algorithm is considered.
It has been implemented and the numerical results have been obtained for 
well-known systems.

[Contact e-mail]
nataly@is1483.spb.edu