# On backward stability of holomorphic dynamical systems

Fundamenta Mathematicae (1998)

- Volume: 158, Issue: 2, page 97-107
- ISSN: 0016-2736

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topLevin, Genadi.. "On backward stability of holomorphic dynamical systems." Fundamenta Mathematicae 158.2 (1998): 97-107. <http://eudml.org/doc/212311>.

@article{Levin1998,

abstract = {For a polynomial with one critical point (maybe multiple), which does not have attracting or neutral periodic orbits, we prove that the backward dynamics is stable provided the Julia set is locally connected. The latter is proved to be equivalent to the non-existence of a wandering continuum in the Julia set or to the shrinking of Yoccoz puzzle-pieces to points.},

author = {Levin, Genadi.},

journal = {Fundamenta Mathematicae},

keywords = {critical point; attracting periodic orbits; neutral periodic orbits; Julia set; locally connected; wandering continuum; Yoccoz puzzle-pieces},

language = {eng},

number = {2},

pages = {97-107},

title = {On backward stability of holomorphic dynamical systems},

url = {http://eudml.org/doc/212311},

volume = {158},

year = {1998},

}

TY - JOUR

AU - Levin, Genadi.

TI - On backward stability of holomorphic dynamical systems

JO - Fundamenta Mathematicae

PY - 1998

VL - 158

IS - 2

SP - 97

EP - 107

AB - For a polynomial with one critical point (maybe multiple), which does not have attracting or neutral periodic orbits, we prove that the backward dynamics is stable provided the Julia set is locally connected. The latter is proved to be equivalent to the non-existence of a wandering continuum in the Julia set or to the shrinking of Yoccoz puzzle-pieces to points.

LA - eng

KW - critical point; attracting periodic orbits; neutral periodic orbits; Julia set; locally connected; wandering continuum; Yoccoz puzzle-pieces

UR - http://eudml.org/doc/212311

ER -

## References

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