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

2017
*
arXiv
*
pre-print

Finally, we present some examples for which our results yield

arXiv:1702.02870v3
fatcat:xgdmkt7hznhqrmhg5smjf5fxcm
*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. ...##
###
Contributions to the ergodic theory of hyperbolic flows: unique ergodicity for quasi-invariant measures and equilibrium states for the time-one map
[article]

2021
*
arXiv
*
pre-print

In

arXiv:2103.07333v2
fatcat:upwbxjyrfnapdc6sbnnxskn65q
*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. ...##
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Uniqueness of the measure of maximal entropy for singular hyperbolic flows in dimension 3 and more results on equilibrium states
[article]

2019
*
arXiv
*
pre-print

We give a condition

arXiv:1905.06202v1
fatcat:5ph2ehcbujaxfkkswf4gkga4zy
*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. ...##
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Uniqueness in the Weakly Inelastic Regime of the Equilibrium State to the Boltzmann Equation Driven by a Particle Bath

2011
*
SIAM Journal on Mathematical Analysis
*

Our analysis is based

doi:10.1137/110837437
fatcat:sfyxo5k435hohppoxfng6a6ur4
*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 ...##
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Weierstraß-Institut für Angewandte Analysis und Stochastik On existence and uniqueness of the equilibrium state for an improved Nernst-Planck-Poisson system

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. ...

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

2010
*
Annales de l'Institut Henri Poincare. Analyse non linéar
*

If

doi:10.1016/j.anihpc.2009.10.002
fatcat:wsffamlyhfbnrdhr6yqpdbfx6i
*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 ...##
###
The Castle on the Hill

2000
*
Review of economic dynamics (Print)
*

In this game

doi:10.1006/redy.2000.0094
fatcat:olfgpqpibjh2vew7mhil46ta7u
*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*. ...##
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Real Balance Effects, Timing, and Equilibrium Determination

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". ...

##
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On uniquely implementing cooperation in the prisoners' dilemma

1996
*
Economic Theory
*

In particular, any 2-

doi:10.1007/bf01211822
fatcat:qfal3apauzhf5pqu35qnx6u3ym
*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*...##
###
SUFFICIENT CONDITIONS FOR THE EXISTENCE OF A UNIQUE AND STABLE EQUILIBRIUM STATE OF AN ADIABATIC TUBULAR REACTOR WITH RECYCLE

1970
*
Journal of Chemical Engineering of Japan
*

for

doi:10.1252/jcej.3.248
fatcat:h2azotuqcrgbbazrmdxxivavka
*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*...##
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On uniquely implementing cooperation in the prisoners' dilemma

1997
*
Economic Theory
*

In particular, any 2-

doi:10.1007/bf01213809
fatcat:kqavgq7wqjac3lieyqflxadntu
*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*...##
###
Monetary Policy with State Contingent Interest Rates

2004
*
Social Science Research Network
*

A policy that pegs

doi:10.2139/ssrn.639244
fatcat:3bwdyw3x3jabldeirxekbyzn34
*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 ...##
###
On the use of "small external fields" in the problem of symmetry breakdown in statistical mechanics

1972
*
Annals of Physics
*

We study

doi:10.1016/0003-4916(72)90181-9
fatcat:tqqiq746ivbrllclf6hvzb27cu
*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. ...##
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The K-Property for Subadditive Equilibrium States
[article]

2020
*
arXiv
*
pre-print

By generalizing Ledrappier's criterion for

arXiv:2004.13087v3
fatcat:5m4dt3ob2rhqfafk3zibzuo3x4
*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 ...##
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Ruling Out Multiplicity and Indeterminacy: The Role of Heterogeneity

2000
*
The Review of Economic Studies
*

Second, sufficient heterogeneity leads to

doi:10.1111/1467-937x.00132
fatcat:7pmmlrmhqneftpddttxn2af4gq
*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 ...
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