A thermodynamical formalism describing mechanical interactions

2014 ◽  
Vol 108 (2) ◽  
pp. 20001 ◽  
Author(s):  
R. F. S. Andrade ◽  
A. M. C. Souza ◽  
E. M. F. Curado ◽  
F. D. Nobre
Keyword(s):  
Thermodynamical Formalism

Mechanisms for Phase Transitions in the Multifractal Analysis of Invariant Densities of Correlated Random Maps

1994 ◽  
Vol 49 (12) ◽  
pp. 1219-1222 ◽  
Author(s):  
Günter Radons
Keyword(s):  
Phase Transitions ◽  
Multifractal Analysis ◽  
Random Maps ◽  
Thermodynamical Formalism ◽  
Invariant Densities

Abstract Multifractal properties of the invariant densities of correlated random maps are analyzed. It is proven that within the thermodynamical formalism phase transitions for finite correlations may be due to transients. For systems with infinite correlations we show analytically that phase transitions can occur as a consequence of localization-delocalization transitions of relevant eigenfunctions.

scholarly journals The calculus of thermodynamical formalism

2018 ◽  
Vol 20 (10) ◽  
pp. 2357-2412 ◽  
Author(s):  
Paolo Giulietti ◽  
Benoît Kloeckner ◽  
Artur Lopes ◽  
Diego Marcon
Keyword(s):  
Thermodynamical Formalism

Detecting Phase Transitions in Intermittent Systems by Using the Thermodynamical Formalism

1994 ◽  
Vol 49 (12) ◽  
pp. 1235-1237
Author(s):  
Zoltán Toroczkaia ◽  
Áron Péntek
Keyword(s):  
Fixed Point ◽  
Phase Transitions ◽  
Point Of View ◽  
Stable Fixed Point ◽  
New Classification ◽  
Thermodynamical Formalism ◽  
Generalized Entropies

Abstract Here we illustrate the effectiveness of the thermodynamical formalism applied to a well known chaotic phenomenon, the intermittency. This leads us to a new classification for intermittent phe­nomena from the point of view of the generated chaotic phases in the spectrum of the generalized entropies K (q). New types of intermittencies are found related to the absence or presence of phase transitions with infinite jump in K (q). This is underlined with examples. It is also shown via examples that the existence of a marginally stable fixed point in the system is neither necessary nor sufficient for intermittency.

Thermodynamical formalism for robust classes of potentials and non-uniformly hyperbolic maps

2008 ◽  
Vol 28 (2) ◽  
pp. 501-533 ◽  
Author(s):  
KRERLEY OLIVEIRA ◽  
MARCELO VIANA
Keyword(s):  
Equilibrium State ◽  
Large Class ◽  
Ergodic Theory ◽  
Gibbs Measure ◽  
Transfer Operator ◽  
Operator Approach ◽  
Hölder Continuous ◽  
Thermodynamical Formalism ◽  
Classical Notion ◽  
Positive Eigenfunction

AbstractWe develop a Ruelle–Perron–Fröbenius transfer operator approach to the ergodic theory of a large class of non-uniformly expanding transformations on compact manifolds. For Hölder continuous potentials not too far from constant, we prove that the transfer operator has a positive eigenfunction, which is piecewise Hölder continuous, and use this fact to show that there is exactly one equilibrium state. Moreover, the equilibrium state is a non-lacunary Gibbs measure, a non-uniform version of the classical notion of Gibbs measure that we introduce here.

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