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I will discuss recent progress on understanding the dimension of self-similar sets and measures. The main conjecture in this field is that the only way that the dimension of such a fractal can be "non-full" is if the semigroup of contractions which define it is not free. The result I will discuss is that "non-full" dimension implies "almost non-freeness", in the sense that there are distinct words in the semigroup which are extremely close together (super-exponentially in their lengths). Applications include resolution of some conjectures of Furstenberg on the dimension of sumsets and, together with work of Shmerkin, progress on the absolute continuity of Bernoulli convolutions. The main new ingredient is a statement in additive combinatorics concerning the structure of measures whose entropy does not grow very much under convolution. If time permits I will discuss the analogous results in higher dimensions. I will discuss recent progress on understanding the dimension of self-similar sets and measures. The main conjecture in this field is that the only way that the dimension of such a fractal can be "non-full" is if the semigroup of contractions which define it is not free. The result I will discuss is that "non-full" dimension implies "almost non-freeness", in the sense that there are distinct words in the semigroup which are extremely close ...

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Documents 54H20 | enregistrements trouvés : 86

Dimension of self-similar measures via additive combinatorics Hochman, Mike | CIRM H Nouveau

Seminar on differential equations and dynamical systems II Yorke, J. A. | Springer-Verlag 1970 Nouveau

Symbolic dynamics and its applications :proceedings of the conference on symbolic dynamics and its applications held at Yale university in New Haven#July 28 to August 2 Walters, Peter | American Mathematical Society 1992 Nouveau

Ergodic theory of Zd actions :proceedings of the Warwick symposium#1993-1994 Pollicott, Mark ; Schmidt, Klaus D. | Cambridge University Press 1996 Nouveau

Nielsen theory and dynamical systems :AMS-IMS-SIAM summer research...Mt. Holyoke College in South Hadley, Massachusetts#June 20-26 McCord, Christopher K. | American Mathematical Society 1993 Nouveau

Lectures in differentiable dynamics :expository lectures from the c.b.m.s. regional conference held at case western reserve university cleveland, ohio,june 2-6,1969 Markus, Lawrence | American Mathematical Society 1980 Nouveau

Asymptotic geometric analysis:proceedings of the fall 2010 Fields institute thematic program Ludwig, Monika ; Milman, Vitali D. ; Pestov, Vladimir ; Tomczak-Jaegermann, Nicole | Springer;The Fields Institute for Research in Mathematical Sciences 2013 Nouveau

Topology and dynamics of chaos:in celebration of Robert Gilmore's 70th birthday.Proceedings of the international workshop 'from laser dynamics to topology of chaos'Rouen # june 28-30, 2011 Letellier, Christophe ; Gilmore, Robert | World Scientific 2013 Nouveau

Dynamics and numbers.A special program: Bonn # June 1- July 31, 2014International conference: Bonn # July 21-25, 2014 Kolyada, Sergiy ; Möller, Martin ; Moree, Pieter ; Ward, Thomas | American Mathematical Society 2016 Nouveau

Dynamical numbers.Interplay between dynamical systems and number theory.A special programm, may 1-july 31, 2009International conference, Bonn # july 20-24, 2009 Kolyada, Sergiy ; Manin, Yuri ; Möller, Martin ; Moree, Pieter ; Ward, Thomas | American Mathematical Society 2010 Nouveau

Operator Structures and Dynamical Systems :Satellite Conference of the Fifth European Congress of Mathematics Leiden # July, 21-25, 2008, Jeu, Marcel de ; Silvestrov, Sergei ; Skau, Christian ; Tomiyama, Jun | American Mathematical Society 2009 Nouveau

Descriptive set theory and dynamical systems :based on the international workshop held in Luminy at CIRM#July 1-5 Foreman, M. ; Kechris, A. S. ; Louveau, A. ; Weiss, B. | Cambridge University Press 2000 Nouveau

Ecole d'été de probabilités de Saint-Flour IV - 1974with applications to classical and modern analysis Fernique, X. M. ; Conze, J. P. ; Gani, J. ; Hennequin, P. L. | Springer-Verlag 1975 Nouveau

Topological dynamics and applications :a volume in honor of Robert Ellis. proceedings of a conference in honor of the retirement of Robert Ellis#April 5-6 Dokken, D. P. ; Ellis, D. B. ; Nerurkar, M.G. | American Mathematical Society 1998 Nouveau

Ergodic theoryproceedings of a conference on... held at oberwolfach,germany,june 11-17,1978 Denker, M. ; Jacobs, K. | Springer-Verlag 1979 Nouveau

Combinatorics on wordsprogress and perspectives proceedings of an international meetingAug. 16-22 Cummings, Larry J. | Academic Press 1983 Nouveau

Théorie ergodiqueactes des journées ergodiques Conze, J. P. ; Keane, M. S. | Springer-Verlag 1976 Nouveau

Continuum theory and dynamical systemsproceedings of a joint summer research conference on... was held at humboldt state university#June 17-23 Brown, Morton | American Mathematical Society 1990 Nouveau

Recent advances in topological dynamicsproceedings of the conference on topological dynamics held at Yale University in honor of Professor Gustav Arnold Hedlund on the occasion of his retirementJune 19-23 Beck, Anatole | Springer-Verlag 1973 Nouveau

Dynamical systemsproceedings of the special year held at the university of maryland,college park,1986-87 Alexander, J. | Springer-Verlag 1988 Nouveau

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Symbolic dynamics and its applications :
proceedings of the conference on symbolic dynamics and its applications held at Yale university in New Haven#July 28 to August 2 Walters, Peter | American Mathematical Society 1992 Nouveau

Ergodic theory of Zd actions :
proceedings of the Warwick symposium#1993-1994 Pollicott, Mark ; Schmidt, Klaus D. | Cambridge University Press 1996 Nouveau

Nielsen theory and dynamical systems :
AMS-IMS-SIAM summer research...Mt. Holyoke College in South Hadley, Massachusetts#June 20-26 McCord, Christopher K. | American Mathematical Society 1993 Nouveau

Lectures in differentiable dynamics :
expository lectures from the c.b.m.s. regional conference held at case western reserve university cleveland, ohio,june 2-6,1969 Markus, Lawrence | American Mathematical Society 1980 Nouveau

Asymptotic geometric analysis:
proceedings of the fall 2010 Fields institute thematic program Ludwig, Monika ; Milman, Vitali D. ; Pestov, Vladimir ; Tomczak-Jaegermann, Nicole | Springer;The Fields Institute for Research in Mathematical Sciences 2013 Nouveau

Topology and dynamics of chaos:
in celebration of Robert Gilmore's 70th birthday.
Proceedings of the international workshop 'from laser dynamics to topology of chaos'
Rouen # june 28-30, 2011 Letellier, Christophe ; Gilmore, Robert | World Scientific 2013 Nouveau

Dynamics and numbers.
A special program: Bonn # June 1- July 31, 2014
International conference: Bonn # July 21-25, 2014 Kolyada, Sergiy ; Möller, Martin ; Moree, Pieter ; Ward, Thomas | American Mathematical Society 2016 Nouveau

Dynamical numbers.
Interplay between dynamical systems and number theory.
A special programm, may 1-july 31, 2009
International conference, Bonn # july 20-24, 2009 Kolyada, Sergiy ; Manin, Yuri ; Möller, Martin ; Moree, Pieter ; Ward, Thomas | American Mathematical Society 2010 Nouveau

Operator Structures and Dynamical Systems :
Satellite Conference of the Fifth European Congress of Mathematics
Leiden # July, 21-25, 2008, Jeu, Marcel de ; Silvestrov, Sergei ; Skau, Christian ; Tomiyama, Jun | American Mathematical Society 2009 Nouveau

Descriptive set theory and dynamical systems :
based on the international workshop held in Luminy at CIRM#July 1-5 Foreman, M. ; Kechris, A. S. ; Louveau, A. ; Weiss, B. | Cambridge University Press 2000 Nouveau

Ecole d'été de probabilités de Saint-Flour IV - 1974
with applications to classical and modern analysis Fernique, X. M. ; Conze, J. P. ; Gani, J. ; Hennequin, P. L. | Springer-Verlag 1975 Nouveau

Topological dynamics and applications :
a volume in honor of Robert Ellis. proceedings of a conference in honor of the retirement of Robert Ellis#April 5-6 Dokken, D. P. ; Ellis, D. B. ; Nerurkar, M.G. | American Mathematical Society 1998 Nouveau

Ergodic theory
proceedings of a conference on... held at oberwolfach,germany,june 11-17,1978 Denker, M. ; Jacobs, K. | Springer-Verlag 1979 Nouveau

Combinatorics on words
progress and perspectives proceedings of an international meeting
Aug. 16-22 Cummings, Larry J. | Academic Press 1983 Nouveau

Théorie ergodique
actes des journées ergodiques Conze, J. P. ; Keane, M. S. | Springer-Verlag 1976 Nouveau

Continuum theory and dynamical systems
proceedings of a joint summer research conference on... was held at humboldt state university#June 17-23 Brown, Morton | American Mathematical Society 1990 Nouveau

Recent advances in topological dynamics
proceedings of the conference on topological dynamics held at Yale University in honor of Professor Gustav Arnold Hedlund on the occasion of his retirement
June 19-23 Beck, Anatole | Springer-Verlag 1973 Nouveau

Dynamical systems
proceedings of the special year held at the university of maryland,college park,1986-87 Alexander, J. | Springer-Verlag 1988 Nouveau