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The study of the path-connectedness of the space of $C^{r}$ actions of $\mathbb{Z}^{2}$ on the interval [0,1] plays an important role in the classification of codimension 1 foliations on 3 manifolds. One way to deform actions is by conjugation. If an action can be brought arbitrarily close to the trivial one by conjugation, it is said to be quasi-reducible. In this talk, we will present and compare obstructions to quasi-reducibility in different regularity classes, and draw conclusions concerning the initial connectedness problem.[-]

The study of the path-connectedness of the space of $C^{r}$ actions of $\mathbb{Z}^{2}$ on the interval [0,1] plays an important role in the classification of codimension 1 foliations on 3 manifolds. One way to deform actions is by conjugation. If an action can be brought arbitrarily close to the trivial one by conjugation, it is said to be quasi-reducible. In this talk, we will present and compare obstructions to quasi-reducibility in different ...[+]

37C05 ; 37C10 ; 37C15 ; 37E05 ; 37E10 ; 57S25

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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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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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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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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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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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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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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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The notion of singular hyperbolicity for vector fields has been introduced by Morales, Pacifico and Pujals in order to extend the classical uniform hyperbolicity and include the presence of singularities. This covers the Lorenz attractor. I will present a joint work with Dawei Yang which proves a dichotomy in the space of three-dimensional $C^{1}$-vector fields, conjectured by J. Palis: every three-dimensional vector field can be $C^{1}$-approximated by one which is singular hyperbolic or by one which exhibits a homoclinic tangency.[-]

The notion of singular hyperbolicity for vector fields has been introduced by Morales, Pacifico and Pujals in order to extend the classical uniform hyperbolicity and include the presence of singularities. This covers the Lorenz attractor. I will present a joint work with Dawei Yang which proves a dichotomy in the space of three-dimensional $C^{1}$-vector fields, conjectured by J. Palis: every three-dimensional vector field can be $C^{1}...[+]

37C29 ; 37Dxx ; 37C10 ; 37F15

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Documents 37C10 9 résultats

Connectedness and deformation by conjugation of actions on [0,1] (or $^1) - Eynard-Bontemps, Hélène (Auteur de la Conférence) | CIRM H Nouveau

Contact flows and Birkhoff sections - Part 2 - Vaugon, Anne (Auteur de la Conférence) ; Dehornoy, Pierre (Auteur de la Conférence) | CIRM H Nouveau

Anosov flows in 3 dimensions and Anosov-like actions - Part 2 - Mann, Kathryn (Auteur de la Conférence) ; Barthelmé, Thomas (Auteur de la Conférence) | CIRM H Nouveau

Anosov flows in 3 dimensions and Anosov-like actions - Part 1 - Mann, Kathryn (Auteur de la Conférence) ; Barthelmé, Thomas (Auteur de la Conférence) | CIRM H Nouveau

Contact flows and Birkhoff sections - Part 1 - Vaugon, Anne (Auteur de la Conférence) ; Dehornoy, Pierre (Auteur de la Conférence) | CIRM H Nouveau

Anosov flows in 3 dimensions and Anosov-like actions - Part 3 - Mann, Kathryn (Auteur de la Conférence) ; Barthelmé, Thomas (Auteur de la Conférence) | CIRM H Nouveau

Contact flows and Birkhoff sections - Part 3 - Vaugon, Anne (Auteur de la Conférence) ; Dehornoy, Pierre (Auteur de la Conférence) | CIRM H Nouveau

Which geodesic flows are left-handed? - Dehornoy, Pierre (Auteur de la Conférence) | CIRM H Nouveau

Singular hyperbolicity and homoclinic tangencies of 3-dimensional flows - Crovisier, Sylvain (Auteur de la Conférence) | CIRM H Nouveau