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# Documents  37FXX | enregistrements trouvés : 21

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## Emergence of wandering stable components Berger, Pierre | CIRM H

Post-edited

Research talks;Dynamical Systems and Ordinary Differential Equations

In a joint work with Sebastien Biebler, we show the existence of a locally dense set of real polynomial automorphisms of $\mathbb{C}^{2}$ displaying a stable wandering Fatou component; in particular this solves the problem of their existence, reported by Bedford and Smillie in 1991. These wandering Fatou components have non-empty real trace and their statistical behavior is historical with high emergence. The proof follows from a real geometrical model which enables us to show the existence of an open and dense set of $C^{r}$ families of surface diffeomorphisms in the Newhouse domain, each of which displaying a historical, high emergent, wandering domain at a dense set of parameters, for every $2\leq r\leq \infty$ and $r=\omega$. Hence, this also complements the recent work of Kiriki and Soma, by proving the last Taken's problem in the $C^{\infty }$ and $C^{\omega }$-case. In a joint work with Sebastien Biebler, we show the existence of a locally dense set of real polynomial automorphisms of $\mathbb{C}^{2}$ displaying a stable wandering Fatou component; in particular this solves the problem of their existence, reported by Bedford and Smillie in 1991. These wandering Fatou components have non-empty real trace and their statistical behavior is historical with high emergence. The proof follows from a real g...

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## The Mandelbrot set, theme and variations Lei, Tan | Cambridge University Press 2000

Congrès

- 363 p.
ISBN 978-0-521-77476-5

London mathematical society lecture note series , 0274

Localisation : Collection 1er étage

composition de fonction analytique # ensemble de Mandelbrot # espace de Julia quadratique # itération # système dynamique # système dynamique complexe # équation fonctionnelle dans un domaine complexe

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## Laminations and foliations in dynamics, geometry and topology :proceedings of the conference on ... held at SUNY#May 18-24 Lyubich, Mikhail ; Milnor, John W. ; Minsky, Yair N. | American Mathematical Society 2001

Congrès

- 233 p.
ISBN 978-0-8218-1985-2

Contemporary mathematics , 0269

Localisation : Collection 1er étage

géométrie différentielle # topologie # variété topologique # feuilletage # feuilletage holomorphe # dynamique holomorphe # variété de dimension 3 # singularité de champs de vecteurs holomorphes # lamination # surface de Riemann # fonction méromorphe # uniformisation

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## 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

Congrès

- X-317 p.
ISBN 978-0-8218-4747-3

Contemporary mathematics , 0503

Localisation : Collection 1er étage

théorie des opérateurs # dynamique # système dynamique

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## Holomorphic dynamical systemsLectures given at the C.I.M.E. summer schoolCetraro # july 7-12, 2008 Gentili, Graziano ; Guenot, Jacques ; Patrizio, Giorgio | Springer 2010

Congrès

- xiii; 342 p.
ISBN 978-3-642-13170-7

Lecture notes in mathematics , 1998

Localisation : Collection 1er étage

fonctions holomorphes # dynamique différentiable # système dynamique complexe

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## Conformal dynamics and hyperbolic geometry:conference on conformal dynamics and hyperbolic geometry in honor of Linda Keen's 70th birthday,graduate school and university center of CUNY New York, NY#october 21-23, 2010 Bonahon, Francis ; Devaney, Robert L. ; Gardiner, Frederick P. ; Saric, Dragomir | American Mathematical Society 2012

Congrès

- vii-256 p.
ISBN 978-0-8218-5348-1

Contemporary mathematics , 0573

Localisation : Collection 1er étage

théorie des fonctions géométriques # déformation # géométrie hyperbolique

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## Complex analysis and dynamical systems VI.Part 2: complex analysis, quasiconformal mappings, complex dynamics.Sixth international conference on complex analysis and dynamical systems in honor of David Shoikhet on the occasion of his sixtieth birthdayNahariya # May 19-24, 2013 Agranovsky, Mark L. ; Ben Artzi, Matania ; Galloway, Greg ; Karp, Lavi ; Khavinson, Dmitry ; Reich, Simeon ; Weinstein,Gilbert ; Zalcman, Lawrence | American Mathematical Society;Bar-Ilan University 2016

Congrès

- xxxiii; 316 p.
ISBN 978-1-4704-1703-1

Contemporary mathematics , 0667

Localisation : Collection 1er étage

David Shoiykhet # fonction d'une variable complexe # calcul des variations # analyse numérique

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## Nonlinear analysis with resurgent functions Sauzin, David | CIRM H

Multi angle

Research talks;Dynamical Systems and Ordinary Differential Equations;Algebraic and Complex Geometry

Ecalle’s resurgent functions appear naturally as Borel transforms of divergent series like Stirling series, formal solutions of differential equations like Euler series, or formal series associated with many other problems in Analysis and dynamical systems. Resurgence means a certain property of analytic continuation in the Borel plane, whose stability under con- volution (the Borel counterpart of multiplication of formal series) is not obvious. Following the analytic continuation of the convolution of several resurgent functions is indeed a delicate question, but this must be done in an explicit quan- titative way so as to make possible nonlinear resurgent calculus (e.g. to check that resurgent functions are stable under composition or under substitution into a convergent series). This can be done by representing the analytic continuation of the convolution product as the integral of a holomorphic n-form on a singular n-simplex obtained as a suitable explicit deformation of the standard n-simplex. The theory of currents is convenient to deal with such integrals of holomorphic forms, because it allows to content oneself with little regularity: the deformations we use are only Lipschitz continuous, because they are built from the flow of non-autonomous Lipschitz vector fields. Ecalle’s resurgent functions appear naturally as Borel transforms of divergent series like Stirling series, formal solutions of differential equations like Euler series, or formal series associated with many other problems in Analysis and dynamical systems. Resurgence means a certain property of analytic continuation in the Borel plane, whose stability under con- volution (the Borel counterpart of multiplication of formal series) is not obvious. ...

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## Big mapping class groups - lecture 1 Calegari, Danny | CIRM H

Multi angle

Research schools;Dynamical Systems and Ordinary Differential Equations;Topology

Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. We will describe some properties of the objects involved, and give some fruitful relations between the dynamics of the two actions. For example, we will see that loxodromic elements (for the first action) necessarily have rational rotation number (for the second action). Using these relations, we will explain how to construct non trivial quasimorphisms on subgroups of big mapping class groups. This includes joint work with Alden Walker.
Part II - Examples : In this part we will discuss a number of natural examples in which big mapping class groups and their subgroups arise. These include the inverse limit constructions of de Carvalho-Hall, the theory of finite depth (taut) foliations of 3-manifolds, the theory of “Artinization” of Thompson-like groups, two dimensional smooth dynamics, one dimensional complex dynamics (topology of the shift locus, Schottky spaces) and several other contexts. We will try to indicate how viewing these examples from the perspective of (big) mapping class groups is a worthwhile approach.
Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. We will describe some properties of ...

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## Big mapping class groups - lecture 2 Calegari, Danny | CIRM H

Multi angle

Research schools;Dynamical Systems and Ordinary Differential Equations;Topology

Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. We will describe some properties of the objects involved, and give some fruitful relations between the dynamics of the two actions. For example, we will see that loxodromic elements (for the first action) necessarily have rational rotation number (for the second action). Using these relations, we will explain how to construct non trivial quasimorphisms on subgroups of big mapping class groups. This includes joint work with Alden Walker.
Part II - Examples : In this part we will discuss a number of natural examples in which big mapping class groups and their subgroups arise. These include the inverse limit constructions of de Carvalho-Hall, the theory of finite depth (taut) foliations of 3-manifolds, the theory of “Artinization” of Thompson-like groups, two dimensional smooth dynamics, one dimensional complex dynamics (topology of the shift locus, Schottky spaces) and several other contexts. We will try to indicate how viewing these examples from the perspective of (big) mapping class groups is a worthwhile approach.
Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. We will describe some properties of ...

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## Big mapping class groups - lecture 3 Calegari, Danny | CIRM H

Multi angle

Research schools;Dynamical Systems and Ordinary Differential Equations;Topology

Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. We will describe some properties of the objects involved, and give some fruitful relations between the dynamics of the two actions. For example, we will see that loxodromic elements (for the first action) necessarily have rational rotation number (for the second action). Using these relations, we will explain how to construct non trivial quasimorphisms on subgroups of big mapping class groups. This includes joint work with Alden Walker.
Part II - Examples : In this part we will discuss a number of natural examples in which big mapping class groups and their subgroups arise. These include the inverse limit constructions of de Carvalho-Hall, the theory of finite depth (taut) foliations of 3-manifolds, the theory of “Artinization” of Thompson-like groups, two dimensional smooth dynamics, one dimensional complex dynamics (topology of the shift locus, Schottky spaces) and several other contexts. We will try to indicate how viewing these examples from the perspective of (big) mapping class groups is a worthwhile approach.
Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. We will describe some properties of ...

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## Big mapping class groups - lecture 4 Calegari, Danny | CIRM H

Multi angle

Research schools;Dynamical Systems and Ordinary Differential Equations;Topology

Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. We will describe some properties of the objects involved, and give some fruitful relations between the dynamics of the two actions. For example, we will see that loxodromic elements (for the first action) necessarily have rational rotation number (for the second action). Using these relations, we will explain how to construct non trivial quasimorphisms on subgroups of big mapping class groups. This includes joint work with Alden Walker.
Part II - Examples : In this part we will discuss a number of natural examples in which big mapping class groups and their subgroups arise. These include the inverse limit constructions of de Carvalho-Hall, the theory of finite depth (taut) foliations of 3-manifolds, the theory of “Artinization” of Thompson-like groups, two dimensional smooth dynamics, one dimensional complex dynamics (topology of the shift locus, Schottky spaces) and several other contexts. We will try to indicate how viewing these examples from the perspective of (big) mapping class groups is a worthwhile approach.
Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. We will describe some properties of ...

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## Big mapping class groups - lecture 5 Calegari, Danny | CIRM H

Multi angle

Research schools;Dynamical Systems and Ordinary Differential Equations;Topology

Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. We will describe some properties of the objects involved, and give some fruitful relations between the dynamics of the two actions. For example, we will see that loxodromic elements (for the first action) necessarily have rational rotation number (for the second action). Using these relations, we will explain how to construct non trivial quasimorphisms on subgroups of big mapping class groups. This includes joint work with Alden Walker.
Part II - Examples : In this part we will discuss a number of natural examples in which big mapping class groups and their subgroups arise. These include the inverse limit constructions of de Carvalho-Hall, the theory of finite depth (taut) foliations of 3-manifolds, the theory of “Artinization” of Thompson-like groups, two dimensional smooth dynamics, one dimensional complex dynamics (topology of the shift locus, Schottky spaces) and several other contexts. We will try to indicate how viewing these examples from the perspective of (big) mapping class groups is a worthwhile approach.
Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. We will describe some properties of ...

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## The valuative tree Favre, Charles ; Jonsson, Mattias | Springer 2004

Ouvrage

- 234 p.
ISBN 978-3-540-22984-1

Lecture notes in mathematics , 1853

Localisation : Collection 1er étage

singularité # système dynamique complexe # arbre valuatif # théorie des valuations # valuation de Krull # fonction plurisubharmonique # mesure # topologie sur les arbres

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## Complex dynamics and geometry Cerveau, Dominique ; Ghys, Etienne ; Sibony, Nessim ; Yoccoz, Jean-Christophe | American Mathematical Society 2003

Ouvrage

- 197 p.
ISBN 978-0-8218-3228-8

SMF/AMS texts and monographs , 0010

Localisation : Collection 1er étage

espace de module # fonction théta # théorème de Riemann-Roch # tore complexe # variété abellienne

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## Lectures on quasiconformal mappings Ahlfors, Lars Valerian ; Earle, Clifford J. ; Kra, I. ; Shishikura, Mitsushira | American Mathematical Society 2006

Ouvrage

- 162 p.
ISBN 978-0-8218-3644-6

University lecture series , 0038

Localisation : Collection 1er étage

application quasi-conforme # espace e Teichmuller # système dynamique complexe

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## Fatou, Julia, Montel,le grand prix des sciences mathématiques de 1918, et après... Audin, Michèle | Springer 2009

Ouvrage

- vi; 276 p.
ISBN 978-3-642-00445-2

Localisation : Ouvrage RdC (AUDI)

Fatou, Pierre (1878-1929) # Julia, Gaston (1893-1978) # Montel, Paul (1876-1975) # 20ème siècle # système dynamique complexe

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## Linearization Models for Complex Dynamical Systems : Topics in Univalent Funtions, Functional Equations and Semigroup Theory Elin, Mark ; Shoikhet, David | Birkhäuser 2010

Ouvrage

- xii, 264 p.
ISBN 978-3-0346-0508-3

Operator theory: advances and applications , 0208

Localisation : Collection 1er étage

comportement asymptotique # problème de cauchy # point de Denjoy-Wolff # générateur holomophe # semi-groupe continu

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## Five lectures in complex analysis.Second winter school complex analysis and operator theorySevilla # february 5-9, 2008 Contreras, Manuel D. ; Diaz-Madrigal, Santiago | American Mathematical Society;Real Sociedad Matematica Espanola 2010

Ouvrage

- xiii; 161 p.
ISBN 978-0-8218-4809-8

Contemporary mathematics , 0525

Localisation : Collection 1er étage

fonction d'une variable complexe # théorie des fonctions géométriques # système dynamique complexe # fonction analytique # théorie des fonctions sur le disque # classe spéciale d'opérateur linéaire

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## Early days in complex dynamics:a history of complex dynamics in one variable during 1906-1942 Alexander, Daniel S. ; Iavernaro, Felice ; Rosa, Alessandro | American Mathematical Society;London Mathematical Society 2012

Ouvrage

- xvii; 454 p.
ISBN 978-0-8218-4464-9

History of mathematics , 0038

Localisation : Collection 1er étage

histoire des mathématiques # 19ème siècles # 20ème siècle # système dynamique complexe # fonction d'une variable complexe

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