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Page 2576 of Mathematical Reviews Vol. , Issue 2002D
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<span title="">2002</span>
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state of a system is from its equilibrium state [see J. ...
to that of Axiom A attractors, with stationary states being invariant measures of Sinai-Ruelle-Bowen type (SRB measures). ...
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Page 198 of Mathematical Reviews Vol. 56, Issue 1
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<span title="">1978</span>
<i title="American Mathematical Society">
<a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a>
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The last chapter, “Ergodic theory of Axiom A diffeo- morphisms’’, contains the main results of the book. Let f: M—> M be a C? Axiom A diffeomorphism and let 2, be a basic set for f. ...
The definition of the more general class of Axiom A diffeomorphisms is due to S. Smale. A point x ¢ M is nonwandering if UA U,5.f"U# @ for every neighborhood U of x. ...
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Page 1194 of Mathematical Reviews Vol. 52, Issue 4
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<span title="">1976</span>
<i title="American Mathematical Society">
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From this the author deduces conditions for an Axiom A diffeomorphism to be Bernoulli with respect to equilibrium states, when restricted to basic sets. ...
A-B 276 (1973), A33-A35; MR 47 #6990]. ' S. J. Taylor (Liverpool)
Bowen, Rufus
Bernoulli equilibrium states for Axiom A diffeomorphisms.
Math. Systems Theory 8 (1974/75), no. 4, 289-294. ...
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Equilibrium states for a class of skew products
<span title="2019-05-14">2019</span>
<i title="Cambridge University Press (CUP)">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/t7qnh4dicrhptozut7w2ifbxua" style="color: black;">Ergodic Theory and Dynamical Systems</a>
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We present sufficient conditions, both on the skew products and the potentials, for the existence and uniqueness of equilibrium states, and discuss their statistical stability. ...
We consider skew products on $M\times \mathbb{T}^{2}$ , where $M$ is the two-sphere or the two-torus, which are partially hyperbolic and semi-conjugate to an Axiom A diffeomorphism. ...
Besides, as σ × L is a C 1 Axiom A diffeomorphism and ϕ is Hölder, there is a unique equilibrium state of ϕ with respect to σ × L, which is a Bernoulli probability measure [7] since σ is topologically ...
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Equilibrium states for a class of skew-products
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<span title="2018-08-06">2018</span>
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arXiv
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We consider skew-products on M×T^2, where M is the two-sphere or the two-torus, which are partially hyperbolic and semi-conjugate to an Axiom A diffeomorphism. ...
We present sufficient conditions, both on the skew-products and the potentials, for the existence and uniqueness of equilibrium states, and discuss their statistical stability. ...
Besides, as σ × L is a C 1 Axiom A diffeomorphism and ϕ is Hölder, there is a unique equilibrium state of ϕ with respect to σ × L, which is a Bernoulli probability measure [8] since σ is topologically ...
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Page 4167 of Mathematical Reviews Vol. , Issue 86i
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<span title="">1986</span>
<i title="American Mathematical Society">
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Let M be a closed orientable two-dimensional manifold of genus
p> 1and let f: M — M bea diffeomorphism satisfying Axiom A*
of Smale. ...
Conditions are given for different center manifolds at an equilibrium point to have a nonempty intersection. ...
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Bernoulli equilibrium states for surface diffeomorphisms
<span title="">2011</span>
<i title="American Institute of Mathematical Sciences (AIMS)">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ebeyl2om5vbsrbiuzncpyjustm" style="color: black;">Journal of Modern Dynamics</a>
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Suppose f : M → M is a C 1+α (α > 0) diffeomorphism on a compact smooth orientable manifold M of dimension two, and let µ Ψ be an equilibrium measure for a Hölder continuous potential Ψ : M → R. ...
We show that if µ Ψ has positive metric entropy, then f is measure theoretically isomorphic mod µ Ψ to the product of a Bernoulli scheme and a finite rotation. ...
This was extended by Bowen [B2] to all Axiom A diffeomorphisms, using Parry's characterization of the measure of maximal entropy for a subshift of finite type [Pa] . ...
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Bernoulli equilibrium states for surface diffeomorphisms
<span title="">2011</span>
<i title="American Institute of Mathematical Sciences (AIMS)">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ebeyl2om5vbsrbiuzncpyjustm" style="color: black;">Journal of Modern Dynamics</a>
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Suppose f : M → M is a C 1+α (α > 0) diffeomorphism on a compact smooth orientable manifold M of dimension two, and let µ Ψ be an equilibrium measure for a Hölder continuous potential Ψ : M → R. ...
We show that if µ Ψ has positive metric entropy, then f is measure theoretically isomorphic mod µ Ψ to the product of a Bernoulli scheme and a finite rotation. ...
This was extended by Bowen [B2] to all Axiom A diffeomorphisms, using Parry's characterization of the measure of maximal entropy for a subshift of finite type [Pa] . ...
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Bernoulli equilibrium states for surface diffeomorphisms
[article]
<span title="2011-07-19">2011</span>
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arXiv
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Suppose f is a C^1+α surface diffeomorphism, and m is an equilibrium measure of a Holder continuous potential. ...
We show that if m has positive metric entropy, then f is measure theoretically isomorphic to the product of a Bernoulli scheme and a finite rotation. ...
This was extended by Bowen [B2] to all Axiom A diffeomorphisms, using Parry's characterization of the measure of maximal entropy for a subshift of finite type [Pa] . ...
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The ergodic theory of AxiomA flows
<span title="">1975</span>
<i title="Springer Nature">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/of2b2q3emjhk7dpzwv2fcyfhpa" style="color: black;">Inventiones Mathematicae</a>
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1% is an equilibrium state for qo. ...
So #' is an equilibrium state for ~o*,/~'=#e, and p=p~. Thus/~,~ is the unique equilibrium state. ...
Appendix Throughout what follows A will be a hyperbolic set for the C r flow (ft) on the manifold M (r> 1). We recall that, by assumption, the Riemann metric on M is adapted to fl (see Introduction). ...
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Page 541 of Mathematical Reviews Vol. 54, Issue 2
[page]
<span title="">1977</span>
<i title="American Mathematical Society">
<a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a>
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The paper under review establishes the inequality for an Axiom A no-cycle diffeomorphism by means of an induction argument and a local version of the inequality for a basic set. ...
diffeomorphism of a compact manifold M and let Q be a connected Axiom A attractor (i.e., Q is a closed connected subset of M, fQ=Q, the periodic points of f|Q are dense in Q, Q is a hyperbolic set, and ...
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Symbolic Dynamics for Hyperbolic Flows
<span title="">1973</span>
<i title="JSTOR">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xkzouzjw7zaljamw6gqar2a3di" style="color: black;">American Journal of Mathematics</a>
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For A an « x n matrix of 0's and l's, the set 2 A = {xe2": A X/tXj+l = 1 for all i) is compact and tf-invariant. A basic hyperbolic set A will be closely related to a certain symbolic space I A . ...
the one-dimensional bundle tangent to the flow, and there are constants c, X > 0 so that there is an open set U 3 A with A = fi' e */< ^ Basic hyperbolic sets occur in Smale's Axiom A flows [11], a class ...
We remark that Sinai [10] used the slightly different formalism of Gibbs state. If f t \A is topologically mixing, then the measure fx+ is Bernoulli. ...
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Geometrical constructions of equilibrium states
<span title="2021-09-09">2021</span>
<i title="Cellule MathDoc/CEDRAM">
Mathematics Research Reports
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We also establish very fine statistical properties (Bernoulliness), and we give a characterization of equilibrium states in terms of their conditional measures in the stable/unstable lamination, similar ...
For such systems, we give in particular a constructive proof of the existence of the SRB measure and of the entropy maximizing measure. ...
constructions of equilibrium states ...
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Page 2087 of Mathematical Reviews Vol. , Issue 82e
[page]
<span title="">1982</span>
<i title="American Mathematical Society">
<a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a>
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(The proof is carried out only for the case of the discrete flow generated by a baker’s transformation but the proof for a general Bernoulli system is stated to be similar. ...
A consequence was that neither Q-stability nor Axiom A are C’-generic (r>2) for flows on any surface. ...
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Equilibrium measures, prehistories distributions and fractal dimensions for endomorphisms
<span title="">2012</span>
<i title="American Institute of Mathematical Sciences (AIMS)">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rcpeuakxozcbxkr5eegcbenv4q" style="color: black;">Discrete and Continuous Dynamical Systems. Series A</a>
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These limit measures are in many cases shown to be equal to certain equilibrium measures for Hölder potentials. ...
We study then the 1-sided Bernoullicity (or lack of it) for certain measures invariant to endomorphisms, and give a Classification Theorem for the ergodic and metric types of behaviour of perturbations ...
sided Bernoulli shifts, for various equilibrium measures of the non-invertible system. ...
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