Porcupine-like horseshoes: Transitivity, Lyapunov spectrum, and phase transitions

Lorenzo J. Díaz, and Katrin Gelfert. "Porcupine-like horseshoes: Transitivity, Lyapunov spectrum, and phase transitions." Fundamenta Mathematicae 216.1 (2012): 55-100. <http://eudml.org/doc/282659>.

@article{LorenzoJ2012,
abstract = {We study a partially hyperbolic and topologically transitive local diffeomorphism F that is a skew-product over a horseshoe map. This system is derived from a homoclinic class and contains infinitely many hyperbolic periodic points of different indices and hence is not hyperbolic. The associated transitive invariant set Λ possesses a very rich fiber structure, it contains uncountably many trivial and uncountably many non-trivial fibers. Moreover, the spectrum of the central Lyapunov exponents of $F|_\{Λ\}$ contains a gap and hence gives rise to a first order phase transition. A major part of the proofs relies on the analysis of an associated iterated function system that is genuinely non-contracting.},
author = {Lorenzo J. Díaz, Katrin Gelfert},
journal = {Fundamenta Mathematicae},
keywords = {homoclinic class; Lyapunov exponent; non-contracting iterated function system; partial hyperbolicity; phase transition; spectral gap; skew-product},
language = {eng},
number = {1},
pages = {55-100},
title = {Porcupine-like horseshoes: Transitivity, Lyapunov spectrum, and phase transitions},
url = {http://eudml.org/doc/282659},
volume = {216},
year = {2012},
}

TY - JOUR
AU - Lorenzo J. Díaz
AU - Katrin Gelfert
TI - Porcupine-like horseshoes: Transitivity, Lyapunov spectrum, and phase transitions
JO - Fundamenta Mathematicae
PY - 2012
VL - 216
IS - 1
SP - 55
EP - 100
AB - We study a partially hyperbolic and topologically transitive local diffeomorphism F that is a skew-product over a horseshoe map. This system is derived from a homoclinic class and contains infinitely many hyperbolic periodic points of different indices and hence is not hyperbolic. The associated transitive invariant set Λ possesses a very rich fiber structure, it contains uncountably many trivial and uncountably many non-trivial fibers. Moreover, the spectrum of the central Lyapunov exponents of $F|_{Λ}$ contains a gap and hence gives rise to a first order phase transition. A major part of the proofs relies on the analysis of an associated iterated function system that is genuinely non-contracting.
LA - eng
KW - homoclinic class; Lyapunov exponent; non-contracting iterated function system; partial hyperbolicity; phase transition; spectral gap; skew-product
UR - http://eudml.org/doc/282659
ER -