Self-similarity and the transition from finite to infinite measures in dynamical s...
The transition from finite to infinite measures in dynamical systems
Analysis of Functional Integral Equations, Generalized Ordinary Differential Equat...
| Full text | |
| Author(s): |
Garibaldi, Eduardo
;
Inoquio-Renteria, Irene
Total Authors: 2
|
| Document type: | Journal article |
| Source: | LETTERS IN MATHEMATICAL PHYSICS; v. 112, n. 4, p. 25-pg., 2022-08-01. |
| Abstract | |
We establish an original result for the thermodynamic formalism in the context of expanding circle transformations with an indifferent fixed point. For an observable whose modulus of continuity is linked to the dynamics near such a fixed point, by identifying an appropriate linear space to evaluate the action of the transfer operator, we show that there is a strictly positive eigenfunction associated with the maximal eigenvalue given as the exponential of the topological pressure. Taking into account also the corresponding eigenmeasure, the invariant probability thus obtained is proved to be the unique Gibbs-equilibrium state of the system. (AU) | |
| FAPESP's process: | 19/10485-8 - Gibbs measures for Delone sets |
| Grantee: | Eduardo Garibaldi |
| Support Opportunities: | Regular Research Grants |