C¹-maps having hyperbolic periodic points

N. Aoki; Kazumine Moriyasu; N. Sumi

Fundamenta Mathematicae (2001)

  • Volume: 169, Issue: 1, page 1-49
  • ISSN: 0016-2736

Abstract

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We show that the C¹-interior of the set of maps satisfying the following conditions: (i) periodic points are hyperbolic, (ii) singular points belonging to the nonwandering set are sinks, coincides with the set of Axiom A maps having the no cycle property.

How to cite

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N. Aoki, Kazumine Moriyasu, and N. Sumi. "C¹-maps having hyperbolic periodic points." Fundamenta Mathematicae 169.1 (2001): 1-49. <http://eudml.org/doc/281706>.

@article{N2001,
abstract = { We show that the C¹-interior of the set of maps satisfying the following conditions: (i) periodic points are hyperbolic, (ii) singular points belonging to the nonwandering set are sinks, coincides with the set of Axiom A maps having the no cycle property. },
author = {N. Aoki, Kazumine Moriyasu, N. Sumi},
journal = {Fundamenta Mathematicae},
keywords = {-map; hyperbolic periodic point; Axiom A-map; no cycle property; structural stability},
language = {eng},
number = {1},
pages = {1-49},
title = {C¹-maps having hyperbolic periodic points},
url = {http://eudml.org/doc/281706},
volume = {169},
year = {2001},
}

TY - JOUR
AU - N. Aoki
AU - Kazumine Moriyasu
AU - N. Sumi
TI - C¹-maps having hyperbolic periodic points
JO - Fundamenta Mathematicae
PY - 2001
VL - 169
IS - 1
SP - 1
EP - 49
AB - We show that the C¹-interior of the set of maps satisfying the following conditions: (i) periodic points are hyperbolic, (ii) singular points belonging to the nonwandering set are sinks, coincides with the set of Axiom A maps having the no cycle property.
LA - eng
KW - -map; hyperbolic periodic point; Axiom A-map; no cycle property; structural stability
UR - http://eudml.org/doc/281706
ER -

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