Period doubling, entropy, and renormalization

Jun Hu; Charles Tresser

Fundamenta Mathematicae (1998)

  • Volume: 155, Issue: 3, page 237-249
  • ISSN: 0016-2736

Abstract

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We show that in any family of stunted sawtooth maps, the set of maps whose set of periods is the set of all powers of 2 has no interior point. Similar techniques then allow us to show that, under mild assumptions, smooth multimodal maps whose set of periods is the set of all powers of 2 are infinitely renormalizable with the diameters of all periodic intervals going to zero as the period goes to infinity.

How to cite

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Hu, Jun, and Tresser, Charles. "Period doubling, entropy, and renormalization." Fundamenta Mathematicae 155.3 (1998): 237-249. <http://eudml.org/doc/212254>.

@article{Hu1998,
abstract = {We show that in any family of stunted sawtooth maps, the set of maps whose set of periods is the set of all powers of 2 has no interior point. Similar techniques then allow us to show that, under mild assumptions, smooth multimodal maps whose set of periods is the set of all powers of 2 are infinitely renormalizable with the diameters of all periodic intervals going to zero as the period goes to infinity.},
author = {Hu, Jun, Tresser, Charles},
journal = {Fundamenta Mathematicae},
keywords = {renormalization; topological entropy; sawtooth maps; multimodal maps},
language = {eng},
number = {3},
pages = {237-249},
title = {Period doubling, entropy, and renormalization},
url = {http://eudml.org/doc/212254},
volume = {155},
year = {1998},
}

TY - JOUR
AU - Hu, Jun
AU - Tresser, Charles
TI - Period doubling, entropy, and renormalization
JO - Fundamenta Mathematicae
PY - 1998
VL - 155
IS - 3
SP - 237
EP - 249
AB - We show that in any family of stunted sawtooth maps, the set of maps whose set of periods is the set of all powers of 2 has no interior point. Similar techniques then allow us to show that, under mild assumptions, smooth multimodal maps whose set of periods is the set of all powers of 2 are infinitely renormalizable with the diameters of all periodic intervals going to zero as the period goes to infinity.
LA - eng
KW - renormalization; topological entropy; sawtooth maps; multimodal maps
UR - http://eudml.org/doc/212254
ER -

References

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