Entropy of induced dendrite homeomorphism C(F): C(D) ? C(D)
Por:
Hernández P., Méndez H.
Publicada:
1 ene 2019
Categoría:
Geometry and topology
Resumen:
Let f: D ? D be a dendrite homeomorphism. Let C(D) denote the hyperspace of all subcontinua of D endowed with the Hausdorff metric. Let C(f): C(D) ? C(D) be the induced homeomorphism in hyperspace C(D). We show in this paper that the topological entropy of C(f) has only two possible values: 0 or 8. Also we show that the entropy of C(f) is 8 if and only if there exists a point x ? D such that x is not an element of the minimal subdendrite of D that contains the union a(x, f) ? ?(x, f). © 2019 Topology Proceedings.
Filiaciones:
Hernández P.:
Departamento de Matemáticas, Facultad de Ciencias, UNAM, Ciudad Universitaria, Cd. Mx., C.P. 04510, Mexico
Méndez H.:
Departamento de Matemáticas, Facultad de Ciencias, UNAM, Ciudad Universitaria, Cd. Mx., C.P. 04510, Mexico
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