Acta mathematica Universitatis Comenianae, Tome 70 (2001) no. 2
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P. Sindelarova. A COUNTEREXAMPLE TO A STATEMENT CONCERNING LYAPUNOV STABILITY. Acta mathematica Universitatis Comenianae, Tome 70 (2001) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2001_70_2_a10/
@article{AMUC_2001_70_2_a10,
author = {P. Sindelarova},
title = {A {COUNTEREXAMPLE} {TO} {A} {STATEMENT} {CONCERNING} {LYAPUNOV} {STABILITY}},
journal = {Acta mathematica Universitatis Comenianae},
year = {2001},
volume = {70},
number = {2},
url = {http://geodesic.mathdoc.fr/item/AMUC_2001_70_2_a10/}
}
TY - JOUR
AU - P. Sindelarova
TI - A COUNTEREXAMPLE TO A STATEMENT CONCERNING LYAPUNOV STABILITY
JO - Acta mathematica Universitatis Comenianae
PY - 2001
VL - 70
IS - 2
UR - http://geodesic.mathdoc.fr/item/AMUC_2001_70_2_a10/
ID - AMUC_2001_70_2_a10
ER -
%0 Journal Article
%A P. Sindelarova
%T A COUNTEREXAMPLE TO A STATEMENT CONCERNING LYAPUNOV STABILITY
%J Acta mathematica Universitatis Comenianae
%D 2001
%V 70
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_2001_70_2_a10/
%F AMUC_2001_70_2_a10
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.