Additive, Almost Additive and Asymptotically Additive Potential Sequences Are Equivalent

Cuneo, Noé

doi:10.1007/s00220-020-03780-7

Cited by 18 publications

(27 citation statements)

References 53 publications

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“…In [ 19 ], the author proved that any sequence of almost additive or asymptotically additive potentials is equivalent to standard additive potentials: there exists a continuous potential with the same topological pressure, equilibrium states, variational principle, weak Gibbs measures, level sets (and irregular set) for the Lyapunov exponent and large deviations properties. Yet, it is still unknown wether any sequence of Lipschitz continuous potentials has a Lipschitz continuous additive representative.…”

Section: Preliminariesmentioning

confidence: 99%

Bayes Posterior Convergence for Loss Functions via Almost Additive Thermodynamic Formalism

Lopes

Varandas

2022

J Stat Phys

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Statistical inference can be seen as information processing involving input information and output information that updates belief about some unknown parameters. We consider the Bayesian framework for making inferences about dynamical systems from ergodic observations, where the Bayesian procedure is based on the Gibbs posterior inference, a decision process generalization of standard Bayesian inference (see [ 7 , 37 ]) where the likelihood is replaced by the exponential of a loss function. In the case of direct observation and almost-additive loss functions, we prove an exponential convergence of the a posteriori measures to a limit measure. Our estimates on the Bayes posterior convergence for direct observation are related and extend those in [ 47 ] to a context where loss functions are almost-additive. Our approach makes use of non-additive thermodynamic formalism and large deviation properties [ 39 , 40 , 57 ] instead of joinings.

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Section: Preliminariesmentioning

confidence: 99%

Bayes Posterior Convergence for Loss Functions via Almost Additive Thermodynamic Formalism

Lopes

Varandas

2022

J Stat Phys

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“…Cuneo [13] showed that every almost additive potential sequence is actually equivalent to an additive potential in the sense that there exists a continuous potential with the same equilibrium states, topological pressure, weak Gibbs measures, variational principle, level sets (and irregular set) for the Lyapunov exponent.…”

Section: Ergodic Optimization Of Lyapunov Exponents Of Typical Cocycl...mentioning

confidence: 99%

Entropy of Lyapunov maximizing measures of $SL(2,\mathbb{R})$ typical cocycles

Mohammadpour¹

2021

Preprint

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“…is defined as the topological pressure of F . An important link between asymptotically additive sequences and additive sequences was showed in [11].…”

Section: Asymptotically Additive Sequences Givenmentioning

confidence: 99%

“…[11, Theorem 1.2] Suppose that F = (f n ) n≥1 is a asymptotically additive sequence. Then there exists f ∈ C(X) such thatlim n→+∞ 1 n f n − S n f = 0.Moreover, it was shown in [11, Section 3.1] that F * (µ) = f dµ and P (T, F ) = P (T, f ).…”

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confidence: 99%

Ergodic Optimization Restricted On Certain Subsets Of Invariant Measures

Lin¹,

Tian²

2021

Preprint

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In this article, we pay attention to transitive dynamical systems having the shadowing property and the entropy functions are upper semicontinuous. As for these dynamical systems, when we consider ergodic optimization restricted on the subset of invariant measures whose metric entropy are equal or greater than a given constant, we prove that for generic real continuous functions the ergodic optimization measure is unique, ergodic, full support and have metric entropy equal to the given constant. Similar results also hold for suspension flows over transitive subshift of finite type, C r (r ≥ 2)generic geometric Lorenz attractors and C 1 -generic singular hyperbolic attractors.

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Additive, Almost Additive and Asymptotically Additive Potential Sequences Are Equivalent

Cited by 18 publications

References 53 publications

Bayes Posterior Convergence for Loss Functions via Almost Additive Thermodynamic Formalism

Bayes Posterior Convergence for Loss Functions via Almost Additive Thermodynamic Formalism

Entropy of Lyapunov maximizing measures of $SL(2,\mathbb{R})$ typical cocycles

Ergodic Optimization Restricted On Certain Subsets Of Invariant Measures

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