# International Workshop on Dynamical Systems and Geometry in honor of Prof. Michel Herman

IMPA, Rio de Janeiro, April 9 – 12, 2001

This is a small but very special mathematical conference: it honors Michel Herman, a friend and a great mathematician, who passed away last November. In several ways he became much attached to IMPA, having attended since 1976 many of its conferences, particularly but not only in dynamical systems. He was also a common visitor and in fact he would spend two years with us, starting in early February 2001. One of his last beautiful gestures was to leave to IMPA’s library his more than two thousand mathematical books: a catalog is now being kindly prepared by the University of Paris – Jussieu. He also expressed the wish to have his ashes spread over the city of Rio de Janeiro and this shall take place in the end of the morning of April 10. Details shall be provided later.

Concerning the activities, there will be about six lectures a day from 9 to 12 April of 45 minutes each: three in the morning from 9 to 11:45 a.m. with 15 minutes break between them and three in the afternoon from 14:15 to 17:15 with half an hour break after the first lecture and 15 minutes break afterwards.

**Scientific Programme**

Auditorium Ricardo Mañe |

9:00 – 9:45 |
John Milnor SUNY at Stony Brook |
Dynamics and the Brain. Can dynamical methods help us to understand the functioning of the human brain? A naive report. |

10:00 – 10:45 |
Christian BonattiUniv. Bourgogne |
Recent results on robust transitivity and partial hyperbolicity |

10:00 – 10:45 |
Enrique PujalsUFRJ |
The Dynamics of dominated decomposition |

12:00 – 14:00 |
Lunch |

14:15 – 15:00 |
Patrice Le CalvezUniv. Paris Nord |
Generalized Aubry-Mather sets for non twist maps of the annulus or the torus |

15:00 – 15:30 |
Coffee Break |

15:30 – 16:15 |
Harold RosenbergUniv. Paris VII |
The unicity of the helicoid |

16:30 – 17:15 |
Jean-Paul ThouvenotUniv. Paris VII |
Discontinuities of Lyapunov exponents and a theorem of M. Herman |

Auditorium Ricardo Mañé |

9:00 – 9:45 |
François LaudenbachUniv. Nantes |
About T*(Tand its Lagrangian submanifolds^{n}) |

10:00 – 10:45 |
Anatole KatokPenn. State Univ. |
Liouvillean phenomena in dynamics: Herman’s contribution and some new results |

11:00 – 12:00 |
Ceremony |

12:00 – 14:00 |
Lunch |

14:15 – 15:00 |
Alain ChencinerUniv. Paris VII |
Are the masses of a choreography necessarily equal ? |

15:00 – 15:30 |
Coffee Break |

15:30 – 16:15 |
Ernst HeintzeUniv. Augsburg |
Infinite dimensional symmetric spaces, submanifolds and Kac-Moody algebras |

16:30 – 17:15 |
Viviane BaladiUniv. Paris-Sud |
Dynamical Determinants and Dominated Decomposition in Dimension 2 |

Auditorium Ricardo Mañé |

9:00 – 9:45 |
Albert Fathi ENS – Lyon |
How Michel forced me to turn into PDE’s: Some local results on the Hamilton-Jacobi equation |

10:00 – 10:45 |
Raphael Krikorianֹcole Polytechnique |
About quasi-periodic cocycles |

11:00 – 11:45 |
Jairo BochiIMPA |
Zero Lyapunov exponents |

12:00 – 14:00 |
Lunch |

14:15 – 15:00 |
J.- C. YoccozCollטge de France |
Rational p-adic dynamics, following J. RIVERA-LETELIER |

15:00 – 15:30 |
Coffee Break |

15:30 – 16:15 |
Maurםcio PeixotoIMPA |
Focal stability of geodesics |

16:30 – 17:15 |
Fraחois Ledrappierֹcole Polytechnique |
Ergodic properties of some linear actions |

Auditorium Ricardo Mañé |

9:00 – 9:45 |
John Mather Princeton Univ. |
Differentiability properties of the beta function |

10:00 – 10:45 |
Raphael DouadyENS-Cachan |
Circle diffeomorphisms and automorphic measures |

11:00 – 11:45 |
Carlos G. MoreiraIMPA |
Statistical properties of unimodal maps |

12:00 – 14:00 |
Lunch |

14:15 – 15:00 |
Carlos GutierrezUSP-Sדo Carlos |
Injectivity of C maps ^{1}R at infinity and planar vector fields^{2} –> R^{2} |

15:00 – 15:30 |
Coffee Break |

15:30 – 16:15 |
E. ZehnderETH-Zentrum |
Pseudoholomorphic curves and dynamics in three dimensions |

11:00 – 11:45 |
Hakan EliassonRoyal Inst. Tech. |
Almost reducibility of linear quasi-periodic systems |

**Speakers**

**John Milnor, **SUNY at Stony Brook, Dynamics and the Brain. Can dynamical methods help us to understand the functioning of the human brain? A naive report.

**Christian Bonatti, **Univ. Bourgogne, Recent results on robust transitivity and partial hyperbolicity

** ****Enrique Pujals, **UFRJ, The Dynamics of dominated decomposition

**Patrice Le Calvez, **Univ. Paris Nord, Generalized Aubry-Mather sets for non twist maps of the annulus or the torus

**Harold Rosenberg, **Univ. Paris VII, The unicity of the helicoid

**Jean-Paul Thouvenot, **Univ. Paris VI, Discontinuities of Lyapunov exponents and a theorem of M. Herman

**François Laudenbach, **Univ. Nantes, About *T*(T ^{n}) *and its Lagrangian submanifolds

**Anatole Katok,**Penn. State Univ., Liouvillean phenomena in dynamics: Herman’s contribution and some new results

**Alain Chenciner,**Univ. Paris VII, Are the masses of a choreography necessarily equal?

**Ernst Heintze,**Univ. Augsburg, Infinite dimensional symmetric spaces, submanifolds and Kac-Moody algebras

**Viviane Baladi,**Univ. Paris-Sud, Dynamical Determinants and Dominated Decomposition in Dimension 2

**Albert Fathi**, ENS – Lyon, How Michel forced me to turn into PDE’s: Some local results on the Hamilton-Jacobi equation

**Raphael Krikorian,**École Polytechnique, Quasi-periodic cocycles

**Jairo Bochi,**IMPA, Zero Lyapunov exponents

**J.- C. Yoccoz,**Collège de France, Rational p-adic dynamics, following J. RIVERA-LETELIER

**Maurício Peixot,**IMPA, Focal stability of geodesics

**Fraçois Ledrappier,**École Polytechnique, Ergodic properties of some linear actions

**John Mather**, Princeton Univ. , Differentiability properties of the beta function

**Raphael Douady,**ENS-Cachan, Circle diffeomorphisms and automorphic measures

**Carlos G. Moreira,**IMPA, Statistical properties of unimodal maps

**Carlos Gutierrez,**USP-São Carlos, Injectivity of

*C*maps

^{1}*R*at infinity and planar vector fields

^{2}–> R^{2}**Zehnder,**ETH-Zentrum, Pseudoholomorphic curves and dynamics in three dimensions

**Hakan Eliasson,**Royal Inst. Tech., Almost reducibility of linear quasi-periodic systems

### Participants

Baladi, Viviane Universitè Paris-Sud

Bassam, Fayad École Polytechnique

Bonatti, Christian Université de Bourgogne

Camacho, Cesar IMPA

Carneiro, Mario Jorge Univ. Fed. de Minas Gerais

Chenciner, Alain Univ. Paris VII

Dajczer, Marcos IMPA

De Melo, Welington IMPA

Diaz, Lorenzo PUC-RJ

Do Carmo, Manfredo IMPA

Douady, Raphael Ecole Normale Superieure-Cachan

Heintze, Ernst Univ. Augsburg

Faria, Edson IME/USP

Fathi, Albert Ecole Normale Sup. De Lyon

Flexor, Marguerite Univ. Paris Sud

Florit, Luis IMPA

Gutierrez, Carlos USP/São Carlos

Haefliger, Andre Univ. de Geneve

Hakan, Eliasson Royal Inst. Of Technology

Katok, Anatole Pennsylvania State University

Krikorian, Raphael École Polytechnique

Labarca, Rafael Univ. de Santiago de Chile

Laudenbach, François Univ. de Nantes

Le Calvez, Patrice Univ. Paris Nord

Ledrappier, François École Polytechnique

Lima, Elon Lages IMPA

Lins Neto, Alcides IMPA

Markarian, Roberto Univ. de la Republica

Mather, John Princeton University

Milnor, John SUNY at Stony Brook

Morales, Carlos UFRJ

Moreira, Carlos Gustavo IMPA

Oliveira, Fernando UFMG

Pacífico, Maria José UFRJ

Palis, Jacob IMPA

Peixoto, Maurício IMPA

Pujals, Enrique UFRJ

Ragazzo, Clodoaldo IME/USP

Rios Isabel UFF

Rocha, Luiz Fernando Univ. Fed. Rio Grande do Sul

Rosenberg, Harold Univ. Paris VII

Sotomayor, Jorge IME/USP

Thouvenot, Jean-Paul Univ. Paris VII

Vargas, Edson IME/USP

Viana, Marcelo IMPA

Yoccoz, Jean Christophe Collège de France

Zehnder, Eduard ETH – Zentrum

### Department of Scientific Activities

eventos@impa.br

IMPA, Estrada Dona Castorina 110

22460-320 Rio de Janeiro, Brazil

Fax: +55 (21) 529-5019