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Audiovisual Mathematics Library

Audiovisual Mathematics Library

Documents Hasselblatt, Boris 19 results

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Anosov flows in 3 dimensions and Anosov-like actions - Part 2 - Mann, Kathryn (Author of the conference) ; Barthelmé, Thomas (Author of the conference) | CIRM H

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A (pseudo)-Anosov flow on a 3-manifold can be understood through its orbit space, a bifoliated plane with a natural action of the fundamental group of the manifold. In this minicourse, we will describe techniques to study the dynamics of these orbit space actions as a means to understand the topological theory and the classification of (pseudo)Anosov flows in dimension 3. This leads to a more general theory of 'Anosov-like' actions on bifoliated planes, which form a rich class of discrete dynamical systems including but not limited to the orbit space actions from flows.[-]
A (pseudo)-Anosov flow on a 3-manifold can be understood through its orbit space, a bifoliated plane with a natural action of the fundamental group of the manifold. In this minicourse, we will describe techniques to study the dynamics of these orbit space actions as a means to understand the topological theory and the classification of (pseudo)Anosov flows in dimension 3. This leads to a more general theory of 'Anosov-like' actions on bifoliated ...[+]

37D40 ; 57S25 ; 37B05 ; 37C10 ; 37C27 ; 37D20

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Anosov flows in 3 dimensions and Anosov-like actions - Part 1 - Mann, Kathryn (Author of the conference) ; Barthelmé, Thomas (Author of the conference) | CIRM H

Multi angle

A (pseudo)-Anosov flow on a 3-manifold can be understood through its orbit space, a bifoliated plane with a natural action of the fundamental group of the manifold. In this minicourse, we will describe techniques to study the dynamics of these orbit space actions as a means to understand the topological theory and the classification of (pseudo)Anosov flows in dimension 3. This leads to a more general theory of 'Anosov-like' actions on bifoliated planes, which form a rich class of discrete dynamical systems including but not limited to the orbit space actions from flows.[-]
A (pseudo)-Anosov flow on a 3-manifold can be understood through its orbit space, a bifoliated plane with a natural action of the fundamental group of the manifold. In this minicourse, we will describe techniques to study the dynamics of these orbit space actions as a means to understand the topological theory and the classification of (pseudo)Anosov flows in dimension 3. This leads to a more general theory of 'Anosov-like' actions on bifoliated ...[+]

37D40 ; 57S25 ; 37B05 ; 37C10 ; 37C27 ; 37D20

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Contact flows and Birkhoff sections - Part 1 - Vaugon, Anne (Author of the conference) ; Dehornoy, Pierre (Author of the conference) | CIRM H

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This course is devoted to the interplay of several topological and dynamical notions, namely contact forms and their Reeb flows, open book decompositions, and Anosov flows. We will spend some time explaining the basic definitions and several important examples. The rough plan is (1) Contact forms, Reeb flows, and open book decomposition (2) Birkhoff sections, Anosov flows, and Reeb-Anosov flows.

53D10 ; 37C10 ; 57R65

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Contact flows and Birkhoff sections - Part 3 - Vaugon, Anne (Author of the conference) ; Dehornoy, Pierre (Author of the conference) | CIRM H

Multi angle

This course is devoted to the interplay of several topological and dynamical notions, namely contact forms and their Reeb flows, open book decompositions, and Anosov flows. We will spend some time explaining the basic definitions and several important examples. The rough plan is (1) Contact forms, Reeb flows, and open book decomposition (2) Birkhoff sections, Anosov flows, and Reeb-Anosov flows.

53D10 ; 37C10 ; 57R65

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Precise statistical properties of the geodesic flow on periodic hyperbolic manifolds - Thomine, Damien (Author of the conference) | CIRM H

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37D40 ; 37A50 ; 37D10

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Contact flows and Birkhoff sections - Part 2 - Vaugon, Anne (Author of the conference) ; Dehornoy, Pierre (Author of the conference) | CIRM H

Multi angle

This course is devoted to the interplay of several topological and dynamical notions, namely contact forms and their Reeb flows, open book decompositions, and Anosov flows. We will spend some time explaining the basic definitions and several important examples. The rough plan is (1) Contact forms, Reeb flows, and open book decomposition (2) Birkhoff sections, Anosov flows, and Reeb-Anosov flows.

53D10 ; 37C10 ; 57R65

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Microlocal methods for Anosov flows - Part 1 - Guillarmou, Colin (Author of the conference) | CIRM H

Multi angle

We will introduce some tools from analysis (in particular microlocal analysis) in order to understand the Fredholm theory of Anosov flows. We will then explain how these tools can be used to study a rigidity problem consisting in determining a Riemannian metric from the lengths of its marked closed geodesics, and we will describe a variational approach to study this problem locally near a fixed negatively curved Riemannian metric on a closed manifold.[-]
We will introduce some tools from analysis (in particular microlocal analysis) in order to understand the Fredholm theory of Anosov flows. We will then explain how these tools can be used to study a rigidity problem consisting in determining a Riemannian metric from the lengths of its marked closed geodesics, and we will describe a variational approach to study this problem locally near a fixed negatively curved Riemannian metric on a closed ...[+]

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Microlocal methods for Anosov flows - Part 2 - Guillarmou, Colin (Author of the conference) | CIRM H

Multi angle

We will introduce some tools from analysis (in particular microlocal analysis) in order to understand the Fredholm theory of Anosov flows. We will then explain how these tools can be used to study a rigidity problem consisting in determining a Riemannian metric from the lengths of its marked closed geodesics, and we will describe a variational approach to study this problem locally near a fixed negatively curved Riemannian metric on a closed manifold.[-]
We will introduce some tools from analysis (in particular microlocal analysis) in order to understand the Fredholm theory of Anosov flows. We will then explain how these tools can be used to study a rigidity problem consisting in determining a Riemannian metric from the lengths of its marked closed geodesics, and we will describe a variational approach to study this problem locally near a fixed negatively curved Riemannian metric on a closed ...[+]

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Microlocal methods for Anosov flows - Part 3 - Guillarmou, Colin (Author of the conference) | CIRM H

Multi angle

We will introduce some tools from analysis (in particular microlocal analysis) in order to understand the Fredholm theory of Anosov flows. We will then explain how these tools can be used to study a rigidity problem consisting in determining a Riemannian metric from the lengths of its marked closed geodesics, and we will describe a variational approach to study this problem locally near a fixed negatively curved Riemannian metric on a closed manifold.[-]
We will introduce some tools from analysis (in particular microlocal analysis) in order to understand the Fredholm theory of Anosov flows. We will then explain how these tools can be used to study a rigidity problem consisting in determining a Riemannian metric from the lengths of its marked closed geodesics, and we will describe a variational approach to study this problem locally near a fixed negatively curved Riemannian metric on a closed ...[+]

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Anosov flows in 3 dimensions and Anosov-like actions - Part 3 - Mann, Kathryn (Author of the conference) ; Barthelmé, Thomas (Author of the conference) | CIRM H

Multi angle

A (pseudo)-Anosov flow on a 3-manifold can be understood through its orbit space, a bifoliated plane with a natural action of the fundamental group of the manifold. In this minicourse, we will describe techniques to study the dynamics of these orbit space actions as a means to understand the topological theory and the classification of (pseudo)Anosov flows in dimension 3. This leads to a more general theory of 'Anosov-like' actions on bifoliated planes, which form a rich class of discrete dynamical systems including but not limited to the orbit space actions from flows.[-]
A (pseudo)-Anosov flow on a 3-manifold can be understood through its orbit space, a bifoliated plane with a natural action of the fundamental group of the manifold. In this minicourse, we will describe techniques to study the dynamics of these orbit space actions as a means to understand the topological theory and the classification of (pseudo)Anosov flows in dimension 3. This leads to a more general theory of 'Anosov-like' actions on bifoliated ...[+]

37D40 ; 57S25 ; 37B05 ; 37C10 ; 37C27 ; 37D20

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