UNDECIDABILITY AND CHAOS IN WORD-CODED SYMBOLIC DYNAMICS

Authors
AGNES C RASETTI M
Citation
C. Agnes et M. Rasetti, UNDECIDABILITY AND CHAOS IN WORD-CODED SYMBOLIC DYNAMICS, Chaos, solitons and fractals, 5(2), 1995, pp. 161-175
Citations number
79
Categorie Soggetti
Mathematics,Mechanics,Engineering,"Physics, Applied
Journal title
Chaos, solitons and fractals → ACNP
ISSN journal
09600779
Volume
5
Issue
2
Year of publication
1995
Pages
161 - 175
Database
ISI
SICI code
0960-0779(1995)5:2<161:UACIWS>2.0.ZU;2-5
Abstract
The existence of deterministic chaos in dynamical systems is related w ith Godelian undecidability of a symbolic dynamical system defined in terms of Markov maps associated with the principal congruence subgroup s of the modular group (corresponding to flows on manifold with overal l negative curvature). The main ingredients are the group-orbit word-c oding of the symbolic dynamics, and the Dehn's word problem for the ma pping class group of the manifold.