# Higher-Dimensional Nonlinear Thermodynamic Formalism

@article{Barreira2022HigherDimensionalNT, title={Higher-Dimensional Nonlinear Thermodynamic Formalism}, author={Lu{\'i}s Barreira and Carllos Holanda}, journal={Journal of Statistical Physics}, year={2022} }

Recently, Buzzi and Leplaideur [BL20] introduced a variation of the thermodynamic formalism, which they called nonlinear thermodynamic formalism. Roughly speaking, this amounts to compute the topological pressure replacing Birkhoff sums by images of them under a given function (that may be nonlinear and thus the name). Our main aim is twofold: (1) to introduce a higher-dimensional version of their notion of topological pressure, replacing a potential by a family of potentials, and to establish…

## References

SHOWING 1-10 OF 28 REFERENCES

### Curie–Weiss Type Models for General Spin Spaces and Quadratic Pressure in Ergodic Theory

- Mathematics
- 2020

We extend results on quadratic pressure and convergence of Gibbs measures from Leplaideur and Watbled (Bull Soc Math France 147(2):197–219, 2019) to some general models for spin spaces. We define the…

### Generalized Curie-Weiss-Potts model and quadratic pressure in ergodic theory

- Mathematics
- 2020

We extend results on quadratic pressure and convergence of Gibbs mesures from [14] to the Curie-Weiss-Potts model. We define the notion of equilibrium state for the quadratic pressure and show that…

### Thermodynamic Formalism and Applications to Dimension Theory

- Chemistry
- 2011

Preface.- 1 Introduction.- I Classical Thermodynamic Formalism.- 2 Thermodynamic Formalism: Basic Notions.- 3 The Case of Symbolic Dynamics.- II Nonadditive Thermodynamic Formalism.- 4 Nonadditive…

### Statistical mechanics on a compact set with ^{} action satisfying expansiveness and specification

- Mathematics
- 1973

We consider a compact set Q with a homeomorphism (or more generally a Z' action) such that expansiveness and Bowen's specification condition hold. The entropy is a function on invariant probability…

### Statistical mechanics on a compact set with $Z^\nu $ action satisfying expansiveness and specification

- Mathematics
- 1972

We consider a compact set Q with a homeomorphism (or more generally a Z' action) such that expansiveness and Bowen's specification condition hold. The entropy is a function on invariant probability…

### A shift map with a discontinuous entropy function

- MathematicsDiscrete & Continuous Dynamical Systems - A
- 2020

Let $f:X\to X$ be a continuous map on a compact metric space with finite topological entropy. Further, we assume that the entropy map $\mu\mapsto h_\mu(f)$ is upper semi-continuous. It is well-known…

### Large deviations estimates for dynamical systems without the specification property. Application to the β-shifts

- Mathematics
- 2005

We consider dynamical systems whose sets of orbits verify an approximate product property. This allows us to obtain large deviations results, which were previously proven under the condition of…

### Zeta functions and the periodic orbit structure of hyperbolic dynamics

- Mathematics
- 1990

© Société mathématique de France, 1990, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les…

### The weak specification property for geodesic flows on CAT(–1) spaces

- MathematicsGroups, Geometry, and Dynamics
- 2020

We prove that the geodesic flow on a compact locally CAT(-1) space has the weak specification property, and give various applications. We show that every Holder potential on the space of geodesics…