On the Complexity of Expansive Measures

We prove that the existence of positively expansive measures for continuous maps on compact metric spaces implies the existence of e 〉 0 and a sequence of （m, e）-separated sets whose cardinalities go to infinite as m →∞. We then prove that maps exhibiting such a constant e and the positively expansi...

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Veröffentlicht in:	Acta mathematica Sinica. English series 2015-09, Vol.31 (9), p.1501-1507
1. Verfasser:	Morales, C. A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Complexity Constants Entropy Expansion Mapping Mathematical analysis Mathematics Mathematics and Statistics Metric space Studies 基数复杂性电子紧度量空间膨胀证明连续映射集合
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Zusammenfassung:	We prove that the existence of positively expansive measures for continuous maps on compact metric spaces implies the existence of e 〉 0 and a sequence of （m, e）-separated sets whose cardinalities go to infinite as m →∞. We then prove that maps exhibiting such a constant e and the positively expansive maps share some properties.
ISSN:	1439-8516 1439-7617
DOI:	10.1007/s10114-015-4725-3