ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 70,   2   (2001)
pp.   265-268

A COUNTEREXAMPLE TO A STATEMENT CONCERNING LYAPUNOV STABILITY
P. Sindelarova

Abstract.  We find a class of weakly unimodal $C^\infty$ maps of an interval with zero topological entropy such that no such map f is Lyapunov stable on the set Per(f) of its periodic points. This disproves a statement published in several books and papers, e.g., by V. V. Fedorenko, S.F. Kolyada, A. N. Sharkovsky, A. G. Sivak and J. Smital.

AMS subject classification.  Primary 26A18, 37E05
Keywords.  Topological entropy, Lyapunov stability, periodic points, weakly unimodal maps