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53
Real Analyticity Of Topological Pressure For Parabolically Semihyperbolic Generalized PolynomialLike Maps
 in Indagationes Math
, 2002
"... For arbitrary parabolically semihyperbolic generalized polynomiallike maps f , we prove that on a certain interval, which contains the interval (0; HD(J(f ))), the pressure function t 7! P( t log jf 0 j) is realanalytic. Our results generalize the work of Makarov and Smirnov in [3] and [7]. 1. ..."
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Cited by 9 (2 self)
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For arbitrary parabolically semihyperbolic generalized polynomiallike maps f , we prove that on a certain interval, which contains the interval (0; HD(J(f ))), the pressure function t 7! P( t log jf 0 j) is realanalytic. Our results generalize the work of Makarov and Smirnov in [3] and [7]. 1.
Equilibrium States for Sunimodal Maps
 8 JOS E F. ALVES, V ITOR ARA UJO, AND BENO ^ IT SAUSSOL
, 2001
"... For Sunimodal maps f , we study equilibrium states maximizing the free energies F t () := h() t R log jf 0 jd and the pressure function P (t) := sup F t (). It is shown that if f is uniformly hyperbolic on periodic orbits, then P (t) is analytic for t 1. On the other hand, examples are giv ..."
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Cited by 19 (2 self)
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For Sunimodal maps f , we study equilibrium states maximizing the free energies F t () := h() t R log jf 0 jd and the pressure function P (t) := sup F t (). It is shown that if f is uniformly hyperbolic on periodic orbits, then P (t) is analytic for t 1. On the other hand, examples
NP ae PCP (log n; (log n)
, 2003
"... x \Gamma a j a i \Gamma a j be the polynomial that is 1 at a i and 0 at all a j for j 6= i. Set Uniqueness follows the fact that over a field, every two degree d polynomials either agree on at most d points or agree on all points. 2 Lemma 3 Let jF j ? d. For every set of (d + 1) (point,value ..."
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x \Gamma a j a i \Gamma a j be the polynomial that is 1 at a i and 0 at all a j for j 6= i. Set Uniqueness follows the fact that over a field, every two degree d polynomials either agree on at most d points or agree on all points. 2 Lemma 3 Let jF j ? d. For every set of (d + 1) (point
Math. J. Okayama Univ. 49 (2007), 163{169 PRIVALOV SPACE ON THE UPPER HALF PLANE
"... Abstract. In this paper, we shall consider Privalov space Np0 (D) (p> 1) which consists of holomorphic functions f on the upper half plane D: = fz 2 C j Imz> 0g such that (log+ jf(z)j)p has a harmonic majorant on D. We shall give some properties of Np0 (D). 1. ..."
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Abstract. In this paper, we shall consider Privalov space Np0 (D) (p> 1) which consists of holomorphic functions f on the upper half plane D: = fz 2 C j Imz> 0g such that (log+ jf(z)j)p has a harmonic majorant on D. We shall give some properties of Np0 (D). 1.
ASYMPTOTIC MAXIMUM PRINCIPLE
"... Abstract. By de¯nition the asymptotic maximum principle (AMP) is valid for a class K of analytic functions in the unit disk D if, whenever f 2 K sup 0·µ<2 lim sup r!1 jf(reiµ)j = sup z2D jf(z)j: Let Kt (t ¸ 0) be the class of all f for which lim sup jzj!1 f(1 ¡ jzj)2 log jf(z)jg · t: Then AMP is ..."
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Abstract. By de¯nition the asymptotic maximum principle (AMP) is valid for a class K of analytic functions in the unit disk D if, whenever f 2 K sup 0·µ<2 lim sup r!1 jf(reiµ)j = sup z2D jf(z)j: Let Kt (t ¸ 0) be the class of all f for which lim sup jzj!1 f(1 ¡ jzj)2 log jf(z)jg · t: Then AMP
Real Analyticity of Hausdorff Dimension of Finer Julia Sets of Exponential Family
"... We deal with all the mappings f (z) = e that have an attracting periodic orbit. We consider the set J r (f ) consisting of those points of the Julia set of f that do not escape to in nity under positive iterates of f . Our ultimate result is that the function 7! HD(J r (f )) is real analyti ..."
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Cited by 23 (13 self)
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analytic. In order to prove it we develop the thermodynamic formalism of potentials of the form t log jF j, where F is the natural map associated with f closely related to the corresponding map introduced in [UZd]. It includes appropriately de ned topological pressure, PerronFrobenius operators
Computation at the Heart of Mathematics: Celebrating the Work of David Boyd, Recipient of the 2005 CRMFields Prize
"... One of the great themes of modern number theory is how analysis and algebra often give us the same information by somewhat different means, for example by a formula with an algebraic interpretation on one side and an analytic interpretation on the other.1 There is one such formula that every mathem ..."
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mathematician has been exposed to in their education, but has only recently been seriously interpreted in this way, and that is Jensen’s theorem in complex analysis: This tells us that for a function f which is analytic on a closed disk of radius r, the average value of log jf(z)j on the boundary of the disk
THE ROLE OF THE STREAMBED IN RIVERBANK FILTRATION 38097 fJf
"... ABSTRACT: In an effort to understand the removal characteristics of the Great Miami River’s (GMR) streambed, the Greater Cincinnati Water Works completed a cooperative Flowpath Study with the United States Geological Survey and Miami University in Oxford, Ohio. Twelve monitoring wells were drilled a ..."
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in the river but were never detected in the inclined well. Throughout the study, the streambed demonstrated a range of reductions from 0.5 log to 4 log in the measured parameters. In this riverbank filtration system, the streambed is a significant barrier against infiltration of contaminants. KEY TERMS
Dynamical Zeta Functions For SUnimodal Maps
, 1999
"... . Let f be a nonrenormalizable Sunimodal map. We prove that f is a ColletEckmann map if its dynamical zeta function looks like that of a uniformly hyperbolic map. 1. Introduction A unimodal map f : [0; 1] ! [0; 1] is called Sunimodal if f(0) = f(1) = 0 and if it has nonpositive Schwarzian derivat ..."
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Cited by 2 (0 self)
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derivative Sf = f 000 f 0 \Gamma 3 2 ( f 00 f 0 ) 2 . For such a map set '(x) := log jf 0 (x)j and 'n (x) := '(x) + '(fx) + \Delta \Delta \Delta + '(f n\Gamma1 x). Let \Pi n = fx 2 [0; 1] : f n (x) = xg and define for t 2 R the zeta function i t (z) = exp 1 X n
Logarithmic Sobolev inequalities for some nonlinear PDE's
 Stochastic Processes and their Applications
, 2001
"... The aim of this paper is to study the behavior of solutions of some nonlinear partial differential equations of Mac KeanVlasov type. The main tools used are, on one hand, the logarithmic Sobolev inequality and its connections with the concentration of measure and the transportation inequality with ..."
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Cited by 28 (5 self)
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logarithmic Sobolev inequality with constant C if Ent i f 2 j C Z jrf j 2 d (1) for all smooth enough functions f where Ent i f 2 j = Z f 2 log f 2 d \Gamma Z f 2 d log Z f 2 d : Let us recall two consequences of this property for . First, for every r 0, and every Lipschitz
Results 1  10
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53