scholarly journals Stability in the almost everywhere sense: A linear transfer operator approach

2010 ◽  
Vol 368 (1) ◽  
pp. 144-156 ◽  
Author(s):  
R. Rajaram ◽  
U. Vaidya ◽  
M. Fardad ◽  
B. Ganapathysubramanian
Keyword(s):  
Transfer Operator ◽  
Operator Approach ◽  
Almost Everywhere

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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