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Preprints, Working Papers, ... Year : 2010

DYNAMICAL PROPERTIES OF MONOTONE DENDRITE MAPS

Issam Naghmouchi
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Abstract

We show that for a monotone dendrite map f:D-> D, any w-limit set is either finite or a minimal Cantor set. We also prove that AP(f)=R(f)=\Lambda(f)= cl(P(f)) where cl(P(f)), AP(f), R(f) and \Lambda(f) denote the closure of the set of periodic points, almost periodic points, recurrent points and the union of all w-limit sets respectively. Moreover, we prove that the following properties are equivalent: (i) R(f)=D, (ii) cl(R(f))=D and (iii) D\End(D) is include in P(f).
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Dates and versions

hal-00593321 , version 1 (13-05-2011)
hal-00593321 , version 2 (13-08-2011)

Identifiers

  • HAL Id : hal-00593321 , version 2

Cite

Issam Naghmouchi. DYNAMICAL PROPERTIES OF MONOTONE DENDRITE MAPS. 2010. ⟨hal-00593321v2⟩

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