scholarly journals Entropy approximation versus uniqueness of equilibrium for a dense affine space of continuous functions

2016 ◽  
Vol 16 (06) ◽  
pp. 1650020
Author(s):  
Henri Comman
Keyword(s):  
Invariant Measure ◽  
Equilibrium State ◽  
Affine Space ◽  
Continuous Functions ◽  
Metrizable Space ◽  
Unique Equilibrium ◽  
Space Of Continuous Functions ◽  
Compact Metrizable Space ◽  
Uniqueness Of Equilibrium ◽  
Unique Equilibrium State

We show that for a [Formula: see text]-action (or [Formula: see text]-action) on a non-empty compact metrizable space [Formula: see text], the existence of a affine space dense in the set of continuous functions on [Formula: see text] constituted by elements admitting a unique equilibrium state implies that each invariant measure can be approximated weakly[Formula: see text] and in entropy by a sequence of measures which are unique equilibrium states.

Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow

2013 ◽  
Vol 88 ◽  
pp. 440-451 ◽  
Author(s):  
Tapan K. Sengupta ◽  
Himanshu Singh ◽  
Swagata Bhaumik ◽  
Rajarshi R. Chowdhury
Keyword(s):  
Equilibrium State ◽  
Internal Flow ◽  
Unique Equilibrium ◽  
Unique Equilibrium State

On t-conformal measures and Hausdorff dimension for a family of non-uniformly hyperbolic horseshoes

2009 ◽  
Vol 29 (6) ◽  
pp. 1917-1950 ◽  
Author(s):  
RENAUD LEPLAIDEUR ◽  
ISABEL RIOS
Keyword(s):  
Hausdorff Dimension ◽  
Equilibrium State ◽  
Unstable Manifold ◽  
Markov Partition ◽  
Limit Set ◽  
Unique Equilibrium ◽  
Conformal Measures ◽  
Continuous Potential ◽  
Homoclinic Tangencies ◽  
Unique Equilibrium State

AbstractIn this paper we consider horseshoes with homoclinic tangencies inside the limit set. For a class of such maps, we prove the existence of a unique equilibrium state μt, associated to the (non-continuous) potential −tlog Ju. We also prove that the Hausdorff dimension of the limit set, in any open piece of unstable manifold, is the unique number t0 such that the pressure of μt0 is zero. To deal with the discontinuity of the jacobian, we introduce a countable Markov partition adapted to the dynamics, and work with the first return map defined in a rectangle of it.

scholarly journals Characterization of pseudocompactness by the topology of uniform convergence on function spaces

1978 ◽  
Vol 26 (2) ◽  
pp. 251-256 ◽  
Author(s):  
R. A. McCoy
Keyword(s):  
Uniform Convergence ◽  
Continuous Functions ◽  
Function Spaces ◽  
Metrizable Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Space Of Continuous Functions ◽  
Tychonoff Space ◽  
Necessary And Sufficient

AbstractIt is shown that a Tychonoff space X is pseudocompact if and only if for every metrizable space Y, all uniformities on Y induce the same topology on the space of continuous functions from X into Y. Also for certain pairs of spaces X and Y, a necessary and sufficient condition is established in order that all uniformities on Y induce the same topology on the space of continuous functions from X into Y.

On the Unique Equilibrium State of Tetraploids under Selection

Biometrics ◽  
1996 ◽  
Vol 52 (2) ◽  
pp. 717 ◽  
Author(s):  
M. K. Singh ◽  
Ram A. Kumar
Keyword(s):  
Equilibrium State ◽  
Unique Equilibrium ◽  
Unique Equilibrium State

Periodic solutions to functional differential equations

1985 ◽  
Vol 101 (3-4) ◽  
pp. 253-271 ◽  
Author(s):  
O. A. Arino ◽  
T. A. Burton ◽  
J. R. Haddock
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Continuous Functions ◽  
Ultimate Boundedness ◽  
Space Of Continuous Functions ◽  
Uniform Ultimate Boundedness ◽  
Functional Differential ◽  
Image Position

SynopsisWe consider a system of functional differential equationswhere G: R × B → Rn is T periodic in t and B is a certain phase space of continuous functions that map (−∞, 0[ into Rn. The concepts of B-uniform boundedness and B-uniform ultimate boundedness are introduced, and sufficient conditions are given for the existence of a T-periodic solution to (1.1). Several examples are given to illustrate the main theorem.

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