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On non-uniform specification and uniqueness of the equilibrium state in expansive systems [article]

Ronnie Pavlov
2017 arXiv   pre-print
Finally, we present some examples for which our results yield the first known proof of uniqueness of equilibrium state.  ...  In the former case, we also prove that the unique equilibrium state has the K-property.  ...  Therefore, our original assumption of multiple equilibrium states on X was false, and X has a unique equilibrium state, which we denote by µ.  ... 
arXiv:1702.02870v3 fatcat:xgdmkt7hznhqrmhg5smjf5fxcm

Contributions to the ergodic theory of hyperbolic flows: unique ergodicity for quasi-invariant measures and equilibrium states for the time-one map [article]

Pablo D. Carrasco, Federico Rodriguez-Hertz
2021 arXiv   pre-print
In the same setting, we give a precise characterization of the equilibrium states of the hyperbolic system, showing that existence of a family of Radon measures on the horocyclic foliation such that any  ...  probability (invariant or not) having conditionals given by this family, necessarily is the unique equilibrium state of the system.  ...  Equilibrium States The proof of the above Theorem A relies on the study of equilibrium states for the time-one map of the corresponding hyperbolic flow.  ... 
arXiv:2103.07333v2 fatcat:upwbxjyrfnapdc6sbnnxskn65q

Uniqueness of the measure of maximal entropy for singular hyperbolic flows in dimension 3 and more results on equilibrium states [article]

Renaud Leplaideur
2019 arXiv   pre-print
We give a condition on V which ensures that no singularity can be an equilibrium state. Thus, for these V's, there exists a unique equilibrium state and it is a regular measure.  ...  We prove that any 3-dimensional singular hyperbolic attractor admits for any Hölder continuous potential V at most one equilibrium state for V among regular measures.  ...  Either there is no regular equilibrium state, or there is one, and then it must be unique because it must coincide with the unique local equilibrium on any mille-feuilles.  ... 
arXiv:1905.06202v1 fatcat:5ph2ehcbujaxfkkswf4gkga4zy

Uniqueness in the Weakly Inelastic Regime of the Equilibrium State to the Boltzmann Equation Driven by a Particle Bath

Marzia Bisi, José A. Cañizo, Bertrand Lods
2011 SIAM Journal on Mathematical Analysis  
Our analysis is based on a perturbative argument which uses the knowledge of the stationary solution in the elastic limit and quantitative estimates of the convergence of stationary solutions as the inelasticity  ...  Several qualitative properties of this unique steady state F α are also derived; in particular, we prove that F α is bounded from above and from below by two explicit universal (i.e. independent of α)  ...  It is essentially based on the knowledge of the elastic limit problem and on quantitative estimates of the difference between solutions to the original problem and the equilibrium state in the elastic  ... 
doi:10.1137/110837437 fatcat:sfyxo5k435hohppoxfng6a6ur4

Weierstraß-Institut für Angewandte Analysis und Stochastik On existence and uniqueness of the equilibrium state for an improved Nernst-Planck-Poisson system

Paul Gajewski
2010 Mathematics Subject Classification   unpublished
The thermodynamic equilibrium The aim of this work is to analyse the equations, which describe equilibrium states in the presented model.  ...  The aim of this paper is to give a first existence and uniqueness result for the equilibrium situation.  ... 
fatcat:cimljpreuzberbg7y2s2ehebza

Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps

Paulo Varandas, Marcelo Viana
2010 Annales de l'Institut Henri Poincare. Analyse non linéar  
If the transformation is topologically mixing there is a unique equilibrium state, it is exact and satisfies a non-uniform Gibbs property.  ...  joint work with Marcelo Viana) We prove existence of finitely many ergodic equilibrium states for a large class of non-uniformly expanding local homeomorphisms on compact manifolds and Holder continuous  ...  Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps We prove existence of finitely many ergodic equilibrium states for a large class of non-uniformly expanding local  ... 
doi:10.1016/j.anihpc.2009.10.002 fatcat:wsffamlyhfbnrdhr6yqpdbfx6i

The Castle on the Hill

David K. Levine
2000 Review of economic dynamics (Print)  
In this game of Castle on the Hill, for a broad range of discount factors, including those close to one, equilibrium is unique.  ...  A unique cyclic equilibrium is also possible for intermediate ranges of discount factors. * I would like to thank NSF grant SBER 9617899 and the UCLA Academic Senate for financial support.  ...  In this game of Castle on the Hill, for a broad range of discount factors, including those close to one, equilibrium is unique.  ... 
doi:10.1006/redy.2000.0094 fatcat:olfgpqpibjh2vew7mhil46ta7u

Real Balance Effects, Timing, and Equilibrium Determination

CHRISTIAN A. STOLTENBERG
2012 Journal of Money, Credit and Banking  
On the contrary, when the end-of-period money stock facilitates transactions, the equilibrium displays nominal indeterminacy and equilibrium uniqueness requires an interest rate setting consistent with  ...  Predetermined real money balances can then serve as a state variable, implying that interest rate setting must be passivea violation of the Taylor-principle -for unique, stable, and non-oscillatory equilibrium  ...  This research was supported by the Deutsche Forschungsgemeinschaft through the SFB 649 "Economic Risk".  ... 
doi:10.1111/j.1538-4616.2012.00518.x fatcat:rrvit32vlbcj5n4qtlxnnfsdkm

On uniquely implementing cooperation in the prisoners' dilemma

Bhaskar Chakravorti, John Conley, Bart Taub
1996 Economic Theory  
In particular, any 2-state (and therefore finite) oscillating strategy can generate the folk theorem; moreover, the folk theorem equilibrium set emerges at the same discount factor that yields the unique  ...  One is the stationary solution we discussed in which T is the identity matrix, which remains valid. A second, which we overlooked, is to set which represents oscillation between two states.  ...  In particular, any 2-state (and therefore finite) oscillating strategy can generate the folk theorem; moreover, the folk theorem equilibrium set emerges at the same discount factor that yields the unique  ... 
doi:10.1007/bf01211822 fatcat:qfal3apauzhf5pqu35qnx6u3ym

SUFFICIENT CONDITIONS FOR THE EXISTENCE OF A UNIQUE AND STABLE EQUILIBRIUM STATE OF AN ADIABATIC TUBULAR REACTOR WITH RECYCLE

HISAYOSHI MATSUYAMA
1970 Journal of Chemical Engineering of Japan  
for the Existence of a Unique and Stable Equilibrium State Theorem 2 There exists a unique and stable equilibrium state if any function, C(*), derived from an arbitrary function, W(z), has no zero-point  ...  -L>a (i9) On the other hand, there cannot be more than one asymptotically stable equilibrium state together with no unstable one in such a system that has upper and lower bounds for equilibrium states  ... 
doi:10.1252/jcej.3.248 fatcat:h2azotuqcrgbbazrmdxxivavka

On uniquely implementing cooperation in the prisoners' dilemma

Bhaskar Chakravorti, John Conley, Bart Taub
1997 Economic Theory  
In particular, any 2-state (and therefore finite) oscillating strategy can generate the folk theorem; moreover, the folk theorem equilibrium set emerges at the same discount factor that yields the unique  ...  One is the stationary solution we discussed in which T is the identity matrix, which remains valid. A second, which we overlooked, is to set which represents oscillation between two states.  ...  In particular, any 2-state (and therefore finite) oscillating strategy can generate the folk theorem; moreover, the folk theorem equilibrium set emerges at the same discount factor that yields the unique  ... 
doi:10.1007/bf01213809 fatcat:kqavgq7wqjac3lieyqflxadntu

Monetary Policy with State Contingent Interest Rates

Bernardino Manuel Adão, Isabel H. Correia, Pedro Teles
2004 Social Science Research Network  
A policy that pegs the state-contingent interest rates implements a unique equilibrium globally. We thank Gadi Barlevy and Tom Sargent for comments.  ...  Under a monetary policy rule for the nominal interest rate, i.e. the return on risk-free short-term nominal bonds, there may be a unique local equilibrium, but there are in general multiple global equilibria  ...  We show that while policy on state-noncontingent interest rates is unable to pin down a unique equilibrium, that is not the case when the policy instruments are the returns on state-contingent nominal  ... 
doi:10.2139/ssrn.639244 fatcat:3bwdyw3x3jabldeirxekbyzn34

On the use of "small external fields" in the problem of symmetry breakdown in statistical mechanics

David Ruelle
1972 Annals of Physics  
We study the infinite system equilibrium states in the statistical mechanics of classical lattice gases.  ...  In an appendix we show that an Ising ferromagnet in a nonvanishing magnetic field has only one equilibrium state.  ...  Kaysen for his kind hospitality at the Institute for Advanced Study.  ... 
doi:10.1016/0003-4916(72)90181-9 fatcat:tqqiq746ivbrllclf6hvzb27cu

The K-Property for Subadditive Equilibrium States [article]

Benjamin Call, Kiho Park
2020 arXiv   pre-print
By generalizing Ledrappier's criterion for the K-property of equilibrium states, we extend the criterion to subadditive potentials.  ...  We apply this result to the singular value potentials of matrix cocycles, and show that equilibrium states of large classes of singular value potentials have the K-property.  ...  We would like to thank Ian Morris, Mark Piraino, Anthony Quas, and Cagri Sert for helpful comments, as well as for pointing out an incorrect statement about Bernoulli systems in an earlier version of this  ... 
arXiv:2004.13087v3 fatcat:5m4dt3ob2rhqfafk3zibzuo3x4

Ruling Out Multiplicity and Indeterminacy: The Role of Heterogeneity

Berthold Herrendorf, Akos Valentinyi, Robert Waldmann
2000 The Review of Economic Studies  
Second, sufficient heterogeneity leads to the global saddle-path stability and the uniqueness of a given stationary state and the global uniqueness of equilibrium.  ...  First, sufficient homogeneity with respect to individual productivity leads to the instability and non-uniqueness of a given stationary state and the indeterminacy of equilibrium at that stationary state  ...  Since his models always has a unique equilibrium, he does not, however, study the effects of heterogeneity on the determinacy of equilibrium. 17Note that one might think that a sufficient condition for  ... 
doi:10.1111/1467-937x.00132 fatcat:7pmmlrmhqneftpddttxn2af4gq
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