Eduardo Garibaldi in research grants and scholarships supported by FAPESP.
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Ordered structure is understood in the sense that the structure possesses a low complexity as a quasicrystal, or an aperiodic geometric structure as a tiling or a Delone set, or a computable combinatorial structure as a sub-shift of finite type, a substitution, a recursively enumerable language. A disordered system is understood in the sense that, above a critical value of the temperature…
We intend to develop research on multidimensional thermodynamic formalism and its relations with dynamics, ergodic theory and geometry, paying particular attention to connections with Delone set theory, tilings and Rd-actions. (AU)
The main challenge in the study of freezing phenomena for Gibbs states is to interpret the often complicated entropy behaviour dictated by the associated maximizing probabilities. Actually, the fundamental questions on the recognition of non-convergence of Gibbs measures for exponentially decreasing interactions remain open. In this context, it is particularly challenging to characterize …
(Only some records are available in English at this moment)
This project is dedicated to the study of the zero-temperature convergence of equilibrium states for one-dimensional spin models with a finite number of spin states, with particular emphasis on the case in which the spin variable can take on four distinct values. We consider models whose phase space is the integer lattice Z, where particle interactions occur only between nearest neighbors…
The goal of this project is to study the thermodynamic formalism in zero temperature for Random Dynamical Systems (RDS). We shall make use of already existing results of the literature which (under some hypotheses) guarantee the existence of equilibrium states $\mu_{\beta}$ for random elements $\beta\phi$ in a RDS. We wish to find conditions for $\phi$ to obtain the convergence of $\mu_{\…
The goal of this project is to study sub-actions for Holder continuous potentials on a hyperbolic dynamical system, as well as to characterize the invariant Borel probability measures that maximize the integral of such potentials. We shall make use of the already known theory, like the expansive case, in order to generalize concepts for hyperbolic toral automorphisms.
I plan to continue working on the Bowen-Series coding and use it to study the objects that are related with surfaces with negative curvature. In particular, the exact results of my thesis may allow for precise counting of dynamical quantities like the number of periodic orbits.On another hand, the natural extension of the Bowen-Series transform can be an interesting tool for answering que…
(Only some records are available in English at this moment)
| 1 / 1 | Ongoing grants |
| 6 / 5 | Completed research grants |
| 1 / 1 | Ongoing scholarships in Brazil |
| 4 / 4 | Completed scholarships in Brazil |
| 12 / 11 | All research grants and scholarships |
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