ON FORMAL LANGUAGES IN ONE-DIMENSIONAL DYNAMICAL-SYSTEMS

Authors
XIE HM
Citation
Hm. Xie, ON FORMAL LANGUAGES IN ONE-DIMENSIONAL DYNAMICAL-SYSTEMS, Nonlinearity, 6(6), 1993, pp. 997-1007
Citations number
12
Categorie Soggetti
Mathematics,"Mathematical Method, Physical Science",Mathematics,"Physycs, Mathematical
Journal title
Nonlinearity → ACNP
ISSN journal
09517715
Volume
6
Issue
6
Year of publication
1993
Pages
997 - 1007
Database
ISI
SICI code
0951-7715(1993)6:6<997:OFLIOD>2.0.ZU;2-R
Abstract
We consider the formal languages generated from kneading sequences (KS ) in unimodal maps on an interval. The usefulness of an equivalence re lation R(L) and the Myhill-Nerode theorem in dynamical systems has bee n explored. A necessary and sufficient condition for the languages bei ng regular is proved. The minimal DFA for periodic KS is determined. A simple proof is provided to show that the language of the Feigenbaum attractor is not regular.