Invariant sets with zero measure and full Hausdorff dimension.
Barreira, Luis, Schmeling, Jörg (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Barreira, Luis, Schmeling, Jörg (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Antti Käenmäki, Markku Vilppolainen (2008)
Fundamenta Mathematicae
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It is well known that the open set condition and the positivity of the t-dimensional Hausdorff measure are equivalent on self-similar sets, where t is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions in this respect.
Smorodina, N.V. (2005)
Zapiski Nauchnykh Seminarov POMI
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L. B. Jonker, J. J. P. Veerman (2002)
Fundamenta Mathematicae
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The basic question of this paper is: If you consider two iterated function systems close to each other in an appropriate topology, are the dimensions of their respective invariant sets close to each other? It is well known that the Hausdorff dimension (and Lebesgue measure) of the invariant set does not depend continuously on the iterated function system. Our main result is that (with a restriction on the "non-conformality" of the transformations) the Hausdorff dimension is a lower semicontinuous...
M. V. Jakobson, A. M. Stepin (1989)
Banach Center Publications
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Elisabetta Tornatore, Stefania Maria Buccellato (2007)
Applicationes Mathematicae
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We consider a stochastic SIR system and we prove the existence, uniqueness and positivity of solution. Moreover the existence of an invariant measure under a suitable condition on the coefficients is studied.
Barbu, Dorel, Radu, Viorel (2000)
Novi Sad Journal of Mathematics
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Giuseppe Da Prato (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.
Watson, Neil A. (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Franz Hofbauer, Peter Raith, Thomas Steinberger (2003)
Fundamenta Mathematicae
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The multifractal generalizations of Hausdorff dimension and packing dimension are investigated for an invariant subset A of a piecewise monotonic map on the interval. Formulae for the multifractal dimension of an ergodic invariant measure, the essential multifractal dimension of A, and the multifractal Hausdorff dimension of A are derived.
K. Florek, E. Marczewski, C. Ryll-Nardzewski (1953)
Studia Mathematica
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Xavier Bardina, Carles Rovira, Samy Tindel (2002)
Applicationes Mathematicae
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We find the asymptotic behavior of P(||X-ϕ|| ≤ ε) when X is the solution of a linear stochastic differential equation driven by a Poisson process and ϕ the solution of a linear differential equation driven by a pure jump function.
S. Bernstein, P. Cerejeiras (2007)
Studia Mathematica
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We present necessary and sufficient conditions for a measure to be a p-Carleson measure, based on the Poisson and Poisson-Szegő kernels of the n-dimensional unit ball.
Antal Járai
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CONTENTS§1. Introduction...............................................................5§2. Covariant extension of measures..............................6§3. An invariant extension of Haar measure..................15§4. Covariant extension of Lebesgue measure.............22References....................................................................26
Dedić, Ljuban (2003)
Publications de l'Institut Mathématique. Nouvelle Série
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Antoni Leon Dawidowicz (1989)
Annales Polonici Mathematici
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Antoni Leon Dawidowicz (1992)
Annales Polonici Mathematici
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A method of construction of an invariant measure on a function space is presented.