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Documents 37B05 16 résultats

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Real-analytic manifolds are studied very much in the last century until the time when people found the partition of unity on smooth manifolds makes the manifold theory very tractable. The group of real-analytic diffeomorphisms is the natural automorphism group of the real-analytic manifold. Because of the analytic continuation, there are no partition of unity by functions with support in balls. The germ at a point of a real-analytic diffeomorphism determines the diffeomorphism and hence the group of them looks rigid. However, the group of real-analytic diffeomorphisms is dense in the group of smooth diffeomorphisms and diffeomorphisms can exhibit all kinds of smooth stable dynamics. I would like to convince the audience that the group of real-analytic diffeomorphisms is a really interesting object.In the first course, I would like to review the theorem by Herman which says the identity component of the group of real analytic diffeomorphisms of the n-torus is simple, which gives a motivation to study the group for other manifolds. We also review several fundamental facts in the real analytic category.In the second course, we introduce the regimentation lemma which can play in the real analytic category the role of the partition of unity in the smooth category. For manifolds with nontrivial circle actions, we show that any real analytic diffeomorphism isotopic to the identity is homologous to a diffeomorphism which is an orbitwise rotation.In the third course, we state a lemma which says that the multiple actions of the standard action on the plane is a final (terminal) object in the category of circle actions. This lemma would imply that the identity component of the group of real analytic diffeomorphisms is perfect.[-]
Real-analytic manifolds are studied very much in the last century until the time when people found the partition of unity on smooth manifolds makes the manifold theory very tractable. The group of real-analytic diffeomorphisms is the natural automorphism group of the real-analytic manifold. Because of the analytic continuation, there are no partition of unity by functions with support in balls. The germ at a point of a real-analytic dif...[+]

57R50 ; 57R32 ; 32C05 ; 37C05 ; 37C86 ; 37B05 ; 57R30 ; 54H15

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Real-analytic manifolds are studied very much in the last century until the time when people found the partition of unity on smooth manifolds makes the manifold theory very tractable. The group of real-analytic diffeomorphisms is the natural automorphism group of the real-analytic manifold. Because of the analytic continuation, there are no partition of unity by functions with support in balls. The germ at a point of a real-analytic diffeomorphism determines the diffeomorphism and hence the group of them looks rigid. However, the group of real-analytic diffeomorphisms is dense in the group of smooth diffeomorphisms and diffeomorphisms can exhibit all kinds of smooth stable dynamics. I would like to convince the audience that the group of real-analytic diffeomorphisms is a really interesting object.In the first course, I would like to review the theorem by Herman which says the identity component of the group of real analytic diffeomorphisms of the n-torus is simple, which gives a motivation to study the group for other manifolds. We also review several fundamental facts in the real analytic category.In the second course, we introduce the regimentation lemma which can play in the real analytic category the role of the partition of unity in the smooth category. For manifolds with nontrivial circle actions, we show that any real analytic diffeomorphism isotopic to the identity is homologous to a diffeomorphism which is an orbitwise rotation.In the third course, we state a lemma which says that the multiple actions of the standard action on the plane is a final (terminal) object in the category of circle actions. This lemma would imply that the identity component of the group of real analytic diffeomorphisms is perfect.[-]
Real-analytic manifolds are studied very much in the last century until the time when people found the partition of unity on smooth manifolds makes the manifold theory very tractable. The group of real-analytic diffeomorphisms is the natural automorphism group of the real-analytic manifold. Because of the analytic continuation, there are no partition of unity by functions with support in balls. The germ at a point of a real-analytic dif...[+]

57R50 ; 57R32 ; 32C05 ; 37C05 ; 37C86 ; 37B05 ; 57R30 ; 54H15

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Real-analytic manifolds are studied very much in the last century until the time when people found the partition of unity on smooth manifolds makes the manifold theory very tractable. The group of real-analytic diffeomorphisms is the natural automorphism group of the real-analytic manifold. Because of the analytic continuation, there are no partition of unity by functions with support in balls. The germ at a point of a real-analytic diffeomorphism determines the diffeomorphism and hence the group of them looks rigid. However, the group of real-analytic diffeomorphisms is dense in the group of smooth diffeomorphisms and diffeomorphisms can exhibit all kinds of smooth stable dynamics. I would like to convince the audience that the group of real-analytic diffeomorphisms is a really interesting object.In the first course, I would like to review the theorem by Herman which says the identity component of the group of real analytic diffeomorphisms of the n-torus is simple, which gives a motivation to study the group for other manifolds. We also review several fundamental facts in the real analytic category.In the second course, we introduce the regimentation lemma which can play in the real analytic category the role of the partition of unity in the smooth category. For manifolds with nontrivial circle actions, we show that any real analytic diffeomorphism isotopic to the identity is homologous to a diffeomorphism which is an orbitwise rotation.In the third course, we state a lemma which says that the multiple actions of the standard action on the plane is a final (terminal) object in the category of circle actions. This lemma would imply that the identity component of the group of real analytic diffeomorphisms is perfect.[-]
Real-analytic manifolds are studied very much in the last century until the time when people found the partition of unity on smooth manifolds makes the manifold theory very tractable. The group of real-analytic diffeomorphisms is the natural automorphism group of the real-analytic manifold. Because of the analytic continuation, there are no partition of unity by functions with support in balls. The germ at a point of a real-analytic dif...[+]

57R50 ; 57R32 ; 32C05 ; 37C05 ; 37C86 ; 37B05 ; 57R30 ; 54H15

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Irreducible lattices in semi-simple Lie groups of higher rank are not left-orderable I'll report on the problem of the left orderability of lattices in semi-simple Lie groups, and give some insight of our joint proof with Bertrand Deroin that in rank at least two, an irreducible lattice is not left-orderable. The proof will make use of the tools developed in the minicourse of Bertrand.

20F60 ; 37B05 ; 22F50 ; 37E10 ; 57R30

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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

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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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

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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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

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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y

Space of actions of groups on the real line - Deroin, Bertrand (Auteur de la Conférence) | CIRM H

Multi angle

In these lectures, we will report on some properties of the space of actions of a left-orderable group on the real line. We will notably describe the almost-periodic actions, the harmonic actions and their spaces.

20F60 ; 22F50 ; 37B05 ; 37E10 ; 57R30

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2y
I will present results of three studies, performed in collaboration with M.Benli, L.Bowen, A.Dudko, R.Kravchenko and T.Nagnibeda, concerning the invariant and characteristic random subgroups in some groups of geometric origin, including hyperbolic groups, mapping class groups, groups of intermediate growth and branch groups. The role of totally non free actions will be emphasized. This will be used to explain why branch groups have infinitely many factor representations of type $II_1$.[-]
I will present results of three studies, performed in collaboration with M.Benli, L.Bowen, A.Dudko, R.Kravchenko and T.Nagnibeda, concerning the invariant and characteristic random subgroups in some groups of geometric origin, including hyperbolic groups, mapping class groups, groups of intermediate growth and branch groups. The role of totally non free actions will be emphasized. This will be used to explain why branch groups have infinitely ...[+]

20E08 ; 20F65 ; 37B05

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On some operator-theoretic aspects of ergodic theory - Haase, Markus (Auteur de la Conférence) | CIRM H

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I will describe the main features and methods of a strictly operator-theoretic/functional-analytic perspective on structural ergodic theory in the spirit and in continuation of a recent book project (with T.Eisner, B.Farkas and R.Nagel). The approach is illustrated by a review of some classical results by Abramov on systems with quasi-discrete spectrum and by Veech on compact group extensions (joint work with N.Moriakov).

37A30 ; 37A35 ; 37A55 ; 37B05 ; 47A35 ; 47Nxx ; 22CXX

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