Ruelle operator with nonexpansive IFS

Ka-Sing Lau, and Yuan-Ling Ye. "Ruelle operator with nonexpansive IFS." Studia Mathematica 148.2 (2001): 143-169. <http://eudml.org/doc/284457>.

@article{Ka2001,
abstract = {The Ruelle operator and the associated Perron-Frobenius property have been extensively studied in dynamical systems. Recently the theory has been adapted to iterated function systems (IFS) $(X,\{w_\{j\}\}_\{j=1\}^\{m\},\{p_\{j\}\}_\{j=1\}^\{m\})$, where the $w_\{j\}$’s are contractive self-maps on a compact subset $X ⊆ ℝ^\{d\}$ and the $p_\{j\}$’s are positive Dini functions on X [FL]. In this paper we consider Ruelle operators defined by weakly contractive IFS and nonexpansive IFS. It is known that in such cases, positive bounded eigenfunctions may not exist in general. Our theorems give various sufficient conditions for the existence of such eigenfunctions together with the Perron-Frobenius property.},
author = {Ka-Sing Lau, Yuan-Ling Ye},
journal = {Studia Mathematica},
keywords = {Ruelle operator; nonexpansive map; Perron–Frobenius property; iterated function system; Gibbs measure; weakly contractive map; equicontinuity},
language = {eng},
number = {2},
pages = {143-169},
title = {Ruelle operator with nonexpansive IFS},
url = {http://eudml.org/doc/284457},
volume = {148},
year = {2001},
}

TY - JOUR
AU - Ka-Sing Lau
AU - Yuan-Ling Ye
TI - Ruelle operator with nonexpansive IFS
JO - Studia Mathematica
PY - 2001
VL - 148
IS - 2
SP - 143
EP - 169
AB - The Ruelle operator and the associated Perron-Frobenius property have been extensively studied in dynamical systems. Recently the theory has been adapted to iterated function systems (IFS) $(X,{w_{j}}_{j=1}^{m},{p_{j}}_{j=1}^{m})$, where the $w_{j}$’s are contractive self-maps on a compact subset $X ⊆ ℝ^{d}$ and the $p_{j}$’s are positive Dini functions on X [FL]. In this paper we consider Ruelle operators defined by weakly contractive IFS and nonexpansive IFS. It is known that in such cases, positive bounded eigenfunctions may not exist in general. Our theorems give various sufficient conditions for the existence of such eigenfunctions together with the Perron-Frobenius property.
LA - eng
KW - Ruelle operator; nonexpansive map; Perron–Frobenius property; iterated function system; Gibbs measure; weakly contractive map; equicontinuity
UR - http://eudml.org/doc/284457
ER -