Equilibrium States for Partially Hyperbolic Systems

The name "Thermodynamic formalism" comprises a powerful set of techniques that permit a very fine description of dynamical properties. The sucess of these methods in the context of hyperbolic dynamics is one the major achievements of smooth ergodic theory in the XX century. The problem is that when one relaxes the hyperbolicity hypothesis the panorama becomes much harder to deal with, particularly due to the lack of simple symbolic models.

Together with Federico Rodriguez-Hertz (PSU) we are investigating a different approach to the problem, employing geometrical methods that do not rely on the symbolic description. On the other hand, this new point of view gave us additional perspective in the classical case, allowing us to attack some geometrical problems.



Equilibrium states for center isometries

Pablo D. Carrasco, Federico Rodriguez-Hertz

Journal of the Institute of Mathematics of Jussieu, First view, 2023, pp. 1--61

Geometrical constructions of equilibrium states

Pablo D. Carrasco, Federico Rodriguez Hertz

Mathematics Research Reports, vol. 2, 2021, pp. 45-54


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