Equilibrium states for interval maps: the potential - t log | D f |

Henk Bruin; Mike Todd

Annales scientifiques de l'École Normale Supérieure (2009)

  • Volume: 42, Issue: 4, page 559-600
  • ISSN: 0012-9593

Abstract

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Let f : I → I be a C 2 multimodal interval map satisfying polynomial growth of the derivatives along critical orbits. We prove the existence and uniqueness of equilibrium states for the potential φ t : x ↦ - t log | D f ( x ) | for t close to 1 , and also that the pressure function t ↦ P ( φ t ) is analytic on an appropriate interval near t = 1 .

How to cite

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Bruin, Henk, and Todd, Mike. "Equilibrium states for interval maps: the potential $-t\log |Df|$." Annales scientifiques de l'École Normale Supérieure 42.4 (2009): 559-600. <http://eudml.org/doc/272190>.

@article{Bruin2009,
abstract = {Let $f:I \rightarrow I$ be a $C^2$ multimodal interval map satisfying polynomial growth of the derivatives along critical orbits. We prove the existence and uniqueness of equilibrium states for the potential $\phi _t:x\mapsto -t\log |Df(x)|$ for $t$ close to $1$, and also that the pressure function $t \mapsto P(\phi _t)$ is analytic on an appropriate interval near $t = 1$.},
author = {Bruin, Henk, Todd, Mike},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {equilibrium states; thermodynamic formalism; interval maps; non-uniform hyperbolicity},
language = {eng},
number = {4},
pages = {559-600},
publisher = {Société mathématique de France},
title = {Equilibrium states for interval maps: the potential $-t\log |Df|$},
url = {http://eudml.org/doc/272190},
volume = {42},
year = {2009},
}

TY - JOUR
AU - Bruin, Henk
AU - Todd, Mike
TI - Equilibrium states for interval maps: the potential $-t\log |Df|$
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2009
PB - Société mathématique de France
VL - 42
IS - 4
SP - 559
EP - 600
AB - Let $f:I \rightarrow I$ be a $C^2$ multimodal interval map satisfying polynomial growth of the derivatives along critical orbits. We prove the existence and uniqueness of equilibrium states for the potential $\phi _t:x\mapsto -t\log |Df(x)|$ for $t$ close to $1$, and also that the pressure function $t \mapsto P(\phi _t)$ is analytic on an appropriate interval near $t = 1$.
LA - eng
KW - equilibrium states; thermodynamic formalism; interval maps; non-uniform hyperbolicity
UR - http://eudml.org/doc/272190
ER -

References

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