Geodesic
The behaviour of the nonwandering set of a piecewise monotonic interval map under small perturbations
Mathematica Bohemica, Tome 122 (1997) no. 1, pp. 37-55.

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In this paper piecewise monotonic maps T[0,1]→[0,1] are considered. Let Q be a finite union of open intervals, and consider the set R(Q) of all points whose orbits omit Q. The influence of small perturbations of the endpoints of the intervals in Q on the dynamical system (R(Q),T) is investigated. The decomposition of the nonwandering set into maximal topologically transitive subsets behaves very unstably. Nonetheless, it is shown that a maximal topologically transitive subset cannot be completely destroyed by arbitrary small perturbations of Q. Furthermore it is shown that every sufficiently "big" maximal topologically transitive subset of a sufficiently small perturbation of (R(Q),T) is "dominated" by a topologically transitive subset of (R(Q),T).
DOI : 10.21136/MB.1997.126187
Classification : 37D99, 37E99, 54H20, 58F03, 58F15, 58f30
Mots-clés : piecewise monotonic map; nonwandering set; topologically transitive subset 
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Raith, Peter. The behaviour of the nonwandering set of a piecewise monotonic interval map under small perturbations. Mathematica Bohemica, Tome 122 (1997) no. 1, pp. 37-55. doi : 10.21136/MB.1997.126187. https://geodesic-test.mathdoc.fr/articles/10.21136/MB.1997.126187/

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