| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Fed Rio Grande do Sul, Inst Matemat, BR-91509900 Porto Alegre, RS - Brazil
[2] ICMC USP, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 43, n. 3, p. 467-512, SEP 2012. |
| Web of Science Citations: | 3 |
| Abstract | |
We consider a piecewise analytic real expanding map f: {[}0, 1] -> {[}0, 1] of degree d which preserves orientation, and a real analytic positive potential g: {[}0, 1] -> a{''}e. We assume the map and the potential have a complex analytic extension to a neighborhood of the interval in the complex plane. We also assume log g is well defined for this extension. It is known in Complex Dynamics that under the above hypothesis, for the given potential beta log g, where beta is a real constant, there exists a real analytic eigenfunction I center dot (beta) defined on {[}0, 1] (with a complex analytic extension) for the Ruelle operator of beta log g. Under some assumptions we show that converges and is a piecewise analytic calibrated subaction. Our theory can be applied when log g(x) = -log f'(x). In that case we relate the involution kernel to the so called scaling function. (AU) | |
| FAPESP's process: | 08/02841-4 - Topology, geometry and ergodic theory of dynamical systems |
| Grantee: | Jorge Manuel Sotomayor Tello |
| Support Opportunities: | Research Projects - Thematic Grants |