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Documents  Hasselblatt, Boris | enregistrements trouvés : 17

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Outreach;Mathematics Education and Popularization of Mathematics

Sarah Bray is a PhD student in the Tufts Mathematics Department. She is currently undecided on a specialization topic, although interested in Hyperbolic Geometry and Dynamical Systems. She graduated from Hamilton College in 2011, where she played on the varsity Women’s Lacrosse Team all four years.

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Outreach;Mathematics Education and Popularization of Mathematics

Alexander Bufetov got his Diploma in Mathematics at the Independent University of Moscow in 1999 and his PhD at Princeton University in 2005. After one year as a Postdoctoral student at the University of Chicago, he was employed as an Assistant Professor at Rice University where he also held the 'Edgar Odell Lovett Junior Chair'. In 2009, Alexander Bufetov joined the Steklov Mathematical Institute where he passed his habilitation thesis in order to supervise PhD students. In 2012, he became a CNRS Senior Researcher for the LATP (Laboratoire d’Analyse, Topologie, Probabilités) department at Aix-Marseille University. Alexander Bufetov has received several prizes: a Prize by Moscow Mathematical Society in 2005, a grant by the Sloan Foundation and a grant from the President of the Russian Federation in 2010 and also a grant from the Simons Foundation at the Independent University of Moscow in 2011. His research area is the Ergodic theory of dynamical systems. Alexander Bufetov got his Diploma in Mathematics at the Independent University of Moscow in 1999 and his PhD at Princeton University in 2005. After one year as a Postdoctoral student at the University of Chicago, he was employed as an Assistant Professor at Rice University where he also held the 'Edgar Odell Lovett Junior Chair'. In 2009, Alexander Bufetov joined the Steklov Mathematical Institute where he passed his habilitation thesis in order ...

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Research talks;Dynamical Systems and Ordinary Differential Equations;Topology

Left-handed flows are 3-dimensional flows which have a particular topological property, namely that every pair of periodic orbits is negatively linked. This property (introduced by Ghys in 2007) implies the existence of as many Bikrhoff sections as possible, and therefore allows to reduce the flow to a suspension in many different ways. It then becomes natural to look for examples. A construction of Birkhoff (1917) suggests that geodesic flows are good candidates. In this conference we determine on which hyperbolic orbifolds is the geodesic flow left-handed: the answer is that yes if the surface is a sphere with three cone points, and no otherwise.
dynamical system - geodesic flow - knot - periodic orbit - global section - linking number - fibered knot
Left-handed flows are 3-dimensional flows which have a particular topological property, namely that every pair of periodic orbits is negatively linked. This property (introduced by Ghys in 2007) implies the existence of as many Bikrhoff sections as possible, and therefore allows to reduce the flow to a suspension in many different ways. It then becomes natural to look for examples. A construction of Birkhoff (1917) suggests that geodesic flows ...

37C27 ; 37C15 ; 37C10 ; 57M25

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Outreach;Mathematics Education and Popularization of Mathematics

Boris Hasselblatt held the Jean Morlet Chair from November 2013 to April 2014 with Serge Troubetzkoy (Aix-Marseille Université) as local project leader.
The scientific focus of this Chair is on hyperbolic dynamical systems and related topics. This is a broad and active area of research throughout the world which is on one hand at the core of Boris Hasselblatt's research record and interests and on the other hand well represented in the Marseille region.
Moreover, hyperbolic dynamics has broad interactions with numerous other areas of dynamical systems and mathematics: partial differential equations viewed as infinite-dimensional dynamical systems, celestial mechanics, statistical mechanics, geometry (of nonpositively curved manifolds),Teichmüller theory, topology, to name a few.
In addition, hyperbolic dynamics is important to a broad range of subjects in applied mathematics.
CIRM - Chaire Jean-Morlet 2013 - Aix-Marseille Université
Boris Hasselblatt held the Jean Morlet Chair from November 2013 to April 2014 with Serge Troubetzkoy (Aix-Marseille Université) as local project leader.
The scientific focus of this Chair is on hyperbolic dynamical systems and related topics. This is a broad and active area of research throughout the world which is on one hand at the core of Boris Hasselblatt's research record and interests and on the other hand well represented in the Marseille ...

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Research talks;Analysis and its Applications;Combinatorics;Dynamical Systems and Ordinary Differential Equations

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 ...

28A80 ; 37A10 ; 03D99 ; 54H20

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Research talks;Dynamical Systems and Ordinary Differential Equations

I will present results on the dynamics of horocyclic flows on the unit tangent bundle of hyperbolic surfaces, density and equidistribution properties in particular. I will focus on infinite volume hyperbolic surfaces. My aim is to show how these properties are related to dynamical properties of geodesic flows, as product structure, ergodicity, mixing, ...

37D40

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- 62 p.
ISBN 978-2-85629-786-5

Localisation : Colloque 1er étage (PARI)

dynamique hyperbolique # théorie des nombres # cryptographie

37D40 ; 11T71

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Research talks;Dynamical Systems and Ordinary Differential Equations

I will discuss some recent results with Aaron Brown and Zhiren Wang on actions by higher rank lattices on nilmanifolds. I will present the result in the simplest case possible, $SL(n,Z)$ acting on $Tn$, and try to present the ideas of the proof. The result imply existence of invariant measures for $SL(n,Z)$ actions on $Tn$ with standard homotopy data as well as global rigidity of Ansosov actions on infranilmanifolds and existence of semiconjugacies without assumption on existence of invariant measure. I will discuss some recent results with Aaron Brown and Zhiren Wang on actions by higher rank lattices on nilmanifolds. I will present the result in the simplest case possible, $SL(n,Z)$ acting on $Tn$, and try to present the ideas of the proof. The result imply existence of invariant measures for $SL(n,Z)$ actions on $Tn$ with standard homotopy data as well as global rigidity of Ansosov actions on infranilmanifolds and existence of sem...

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Research talks;Dynamical Systems and Ordinary Differential Equations

37D40 ; 37A50 ; 37D10

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Research talks;Dynamical Systems and Ordinary Differential Equations;Mathematical Physics

We consider the one-parameter families of transfer operators for geodesic flows on negatively curved manifolds. We show that the spectra of the generators have some "band structure" parallel to the imaginary axis. As a special case of "semi-classical" transfer operator, we see that the eigenvalues concentrate around the imaginary axis with some gap on the both sides.

37C30 ; 37D40 ; 53D25 ; 81Q50

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- 458 p.
ISBN 978-0-521-84073-6

Localisation : Ouvrage RdC (Mode)

système dynamique # dynamique hyperbolique # dynamique elliptique # mécanique # théorie ergodique # action de groupe # rigidité # application # Katok

37-06 ; 00B30 ; 22-06 ; 37Dxx

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- 324 p.
ISBN 978-0-521-87541-7

Mathematical sciences research institute publications , 0054

Localisation : Ouvrage RdC (Dyna)

système dynamqies # théorie ergodique # géométrie différentielle # géométrie symplectique quantitative # dynamique hyperbolique # dynamique parabolique

37-06 ; 53-06 ; 00B25

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- vii; 326 p.
ISBN 978-3-319-43058-4

Lecture notes in mathematics , 2164

Localisation : Collection 1er étage

Chaire Jean-Morlet # CIRM # dynamique # théorie ergodique # géométrie différentielle

37C40 ; 37D40 ; 37-06 ; 53-06 ; 37Axx ; 53Cxx

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- 1222 p.
ISBN 978-0-444-52055-5

Localisation : Ouvrage Rdc (Hand)

système dynamique # théorie ergodique # dynamique hyperbolique # dynamique parabolique # système dynamique de dimension infinie # bifurcation homoclinique

37-06 ; 37-00 ; 00B15

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- 1220
ISBN 978-0-444-82669-5

Localisation : Ouvrage RdC (Hand)

système dynamique

37-06 ; 37-02

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- 802 p.
ISBN 978-0-521-34187-5

Encyclopedia of mathematics and its applications , 0054

Localisation : Collection 1er étage

analyse globale et croissance d'orbite # application continu d'intervalle # application lisse d'intervalle # application tordue # comportement non uniformément hyperbolique # comportement statistique d'orbite # difféomorphisme de cercle # dynamique de faible dimension # flot sur surface # homomorphisme du cercle # invariant topologique asymptotique # système dynamique différentielle # système dynamique hyperbolique # système à mesure invariante lisse # théorie ergodique analyse globale et croissance d'orbite # application continu d'intervalle # application lisse d'intervalle # application tordue # comportement non uniformément hyperbolique # comportement statistique d'orbite # difféomorphisme de cercle # dynamique de faible dimension # flot sur surface # homomorphisme du cercle # invariant topologique asymptotique # système dynamique différentielle # système dynamique hyperbolique # système à mesure invariante ...

28Dxx ; 57R50 ; 58F25 ; 58Fxx

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Research talks;Dynamical Systems and Ordinary Differential Equations

37D35 ; 37C30

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