Results 1  10
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99
Existence of Gibbs measures for countable Markov shifts
 Proc. Amer. Math. Soc
, 2003
"... Abstract. We prove that a potential with summable variations and finite pressure on a topologically mixing countable Markov shift has a Gibbs measure iff the transition matrix satisfies the big images and preimages property. This strengthens a result of D. Mauldin and M. Urbański (2001) who showed t ..."
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Cited by 56 (5 self)
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Abstract. We prove that a potential with summable variations and finite pressure on a topologically mixing countable Markov shift has a Gibbs measure iff the transition matrix satisfies the big images and preimages property. This strengthens a result of D. Mauldin and M. Urbański (2001) who showed that this condition is sufficient. 1.
A multifractal analysis for SternBrocot intervals, continued fractions and Diophantine growth rates
, 2005
"... In this paper we obtain multifractal generalizations of classical results by Lévy and Khintchin in metrical Diophantine approximations and measure theory of continued fractions. We give a complete multifractal analysis for Stern–Brocot intervals, for continued fractions and for certain Diophantine ..."
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Cited by 33 (10 self)
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In this paper we obtain multifractal generalizations of classical results by Lévy and Khintchin in metrical Diophantine approximations and measure theory of continued fractions. We give a complete multifractal analysis for Stern–Brocot intervals, for continued fractions and for certain Diophantine growth rates. In particular, we give detailed discussions of two multifractal spectra closely related to the Farey map and the Gauss map.
EQUILIBRIUM MEASURES FOR MAPS WITH INDUCING SCHEMES
, 2008
"... Abstract. We introduce a class of continuous maps f of a compact topological space I admitting inducing schemes and describe the tower constructions associated with them. We then establish a thermodynamic formalism, i.e., describe a class of realvalued potential functions ϕ on I, which admit a uniq ..."
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Cited by 24 (5 self)
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Abstract. We introduce a class of continuous maps f of a compact topological space I admitting inducing schemes and describe the tower constructions associated with them. We then establish a thermodynamic formalism, i.e., describe a class of realvalued potential functions ϕ on I, which admit a unique equilibrium measure µϕ minimizing the free energy for a certain class of invariant measures. We also describe ergodic properties of equilibrium measures including decay of correlation and the central limit theorem. Our results apply to certain maps of the interval with critical points and/or singularities (including some unimodal and multimodal maps) and to potential functions ϕt = −t log df  with t ∈ (t0, t1) for some t0 < 1 < t1. In the particular case of Sunimodal maps we show that one can choose t0 < 0 and that the class of measures under consideration consists of all invariant Borel probability measures. 1.
A multifractal formalism for growth rates and applications to geometrically finite Kleinian groups, Ergodic theory and dynamical systems 24
, 2004
"... ABSTRACT. We elaborate thermodynamic and multifractal formalisms for general classes of potential functions and their average growth rates. We then apply these formalisms to certain geometrically finite Kleinian groups which may have parabolic elements of different ranks. We show that for these gro ..."
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Cited by 22 (12 self)
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ABSTRACT. We elaborate thermodynamic and multifractal formalisms for general classes of potential functions and their average growth rates. We then apply these formalisms to certain geometrically finite Kleinian groups which may have parabolic elements of different ranks. We show that for these groups our revised formalisms give access to a description of the spectrum of ‘homological growth rates ’ in terms of Hausdorff dimension. Furthermore, we derive necessary and sufficient conditions for the existence of ’strong phase transitions’. 1.
Existence and convergence properties of physical measures for certain dynamical systems with holes
 ERGODIC THEORY DYNAM. SYS
, 2010
"... ..."
Zero temperature limits of Gibbsequilibrium states for countable alphabet subshifts of finite type
 J. Stat. Phys
, 2005
"... Let �A be a finitely primitive subshift of finite type on a countable alphabet. For appropriate functions f: �A → IR, the family of Gibbsequilibrium states (µtf)t � 1 for the functions tf is shown to be tight. Any weak ∗accumulation ..."
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Cited by 19 (3 self)
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Let �A be a finitely primitive subshift of finite type on a countable alphabet. For appropriate functions f: �A → IR, the family of Gibbsequilibrium states (µtf)t � 1 for the functions tf is shown to be tight. Any weak ∗accumulation
Statistical properties of onedimensional maps with critical points and singularities
 Stoch. Dyn
"... Abstract. We prove that a class of onedimensional maps with an arbitrary number of nondegenerate critical and singular points admits an induced Markov tower with exponential return time asymptotics. In particular the map has an absolutely continuous invariant probability measure with exponential d ..."
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Cited by 18 (5 self)
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Abstract. We prove that a class of onedimensional maps with an arbitrary number of nondegenerate critical and singular points admits an induced Markov tower with exponential return time asymptotics. In particular the map has an absolutely continuous invariant probability measure with exponential decay of correlations for Hölder observations.
Thermodynamical formalism associated with inducing schemes for onedimensional maps.
 Mosc. Math. J.,
, 2005
"... Abstract. For a smooth map f of a compact interval I admitting an inducing scheme we establish a thermodynamical formalism, i.e., describe a class of realvalued potential functions ϕ on I which admit a unique equilibrium measure µϕ. Our results apply to unimodal maps corresponding to a positive Le ..."
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Cited by 16 (6 self)
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Abstract. For a smooth map f of a compact interval I admitting an inducing scheme we establish a thermodynamical formalism, i.e., describe a class of realvalued potential functions ϕ on I which admit a unique equilibrium measure µϕ. Our results apply to unimodal maps corresponding to a positive Lebesgue measure set of parameters in a oneparameter transverse family.
OrnsteinZernike Theory for the Finite Range Ising Models above ...
, 2001
"... We derive precise OrnsteinZernike asymptotic formula for the decay of the twopoint function (rr0rr)z in the general context of finite range Ising type models on Z a. ..."
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Cited by 15 (5 self)
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We derive precise OrnsteinZernike asymptotic formula for the decay of the twopoint function (rr0rr)z in the general context of finite range Ising type models on Z a.
Projective metrics and mixing properties on towers
 TRANS. AMER. MATH. SOC
, 2001
"... We study the decay of correlations for towers. Using Birkhoff’s projective metrics, we obtain a rate of mixing of the form: cn(f, g) ≤ Ctα(n)‖f‖‖g‖1 where α(n) goes to zero in a way related to the asymptotic mass of upper floors, ‖f ‖ is some Lipschitz norm and ‖g‖1 is some L¹ norm. The fact that ..."
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Cited by 15 (2 self)
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We study the decay of correlations for towers. Using Birkhoff’s projective metrics, we obtain a rate of mixing of the form: cn(f, g) ≤ Ctα(n)‖f‖‖g‖1 where α(n) goes to zero in a way related to the asymptotic mass of upper floors, ‖f ‖ is some Lipschitz norm and ‖g‖1 is some L¹ norm. The fact that the dependence on g is given by an L¹ norm is useful to study asymptotic laws of successive entrance times.