Ruelle operator with nonexpansive IFS

Ka-Sing Lau; Yuan-Ling Ye

Studia Mathematica, Tome 147 (2001), p. 143-169 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $X \subseteq ℝ^{d}$ 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.

Publié le : 2001-01-01

Zbl 1055.37010

EUDML-ID : urn:eudml:doc:284457

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Ka-Sing Lau; Yuan-Ling Ye. Ruelle operator with nonexpansive IFS. Studia Mathematica, Tome 147 (2001) pp. 143-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-2-4/