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• # Artykuł - szczegóły

## Studia Mathematica

2001 | 148 | 2 | 143-169

## Ruelle operator with nonexpansive IFS

EN

### Abstrakty

EN
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.

143-169

wydano
2001

### Twórcy

autor
• Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
autor
• Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
• Department of Mathematics, South China Normal University, Guangzhou 510631, P.R. China