Recent Trends in Nonlinear Science
Sign into February 07, 2020
Introduction
This Advanced Course, apart from being the starting point of the IRP on Low dimensional dynamical systems and applications, will also be the 17th international school of the series Recent Trends in Nonlinear Science by the DANCE (Dinámica, Atractores y Nolinealidad: Caos y Estabilidad) Spanish network.
The school will consist on the following three advanced courses of 9 hours each:
Course 1: Finiteness theorems for limit cycles
by Yu. Ilyashenko
Abstract: A polynomial vector field in the plain has but a finite number of limit cycles. Limit cycles of an analytic vector field cannot accumulate to a polycycle of this field. The first theorem is an immediate corollary of the second one. My current proof consists of the three parts:
- 1. reduction from the ODE to complex analysis
- 2. proofs of the theorems above for vector fields with the so called “alternant” polycycles (those in which the maps TO and FROM central manifolds of the saddlenodes alternate)
- 3. proof for the general case.
There are some gaps in the third part that I am filling now. The lectures will give a brief, yet comprehensive presentation of the first two parts, and a survey of the current state of matters for the third part.
Course 2: Continuity of Lyapunov exponents
by Marcelo Viana
Abstract: I will introduce the notions of linear cocycle and Lyapunov exponent, and will sketch of the proof of the fact that the Lyapunov exponents of random products of matrices vary continuously with the data.
This is based on joint work with C. Bocker, A. Avila and A. Eskin.
Course 3: Dynamical aspects of skew products over minimal dynamics
by Mario Ponce
Abstract: We will introduce the skew-product dynamics, especially those whose transformation in the fibre corresponds to an isometry. We will show how these simple dynamics give rise to several phenomena that are governed both by the arithmetic properties of the rotation numbers, as well as by geometric properties that force some rigid dynamic behaviours. In particular we will study the dynamics associated to invariant sections, to bounded orbits, among other phenomena. These skew-products constitute a geometric model for the resolution of linearised equations of more complex dynamics. We will investigate about the geometric and dynamic methods that allow us to solve such equations.
Poster session
There will be a poster session addressed to young researchers. In order to apply please submit the following form:
Application Form (Closed)
Deadline: December 15th, 2019 (Resolutions will be sent by email by December 20th, 2019).
Organising Committee
| Clara Cufí | Universitat Autònoma de Barcelona |
| Antonio Garijo | Universitat Rovira i Virgili |
| Xavier Jarque | Universitat de Barcelona |
| Jordi Villadelprat | Universitat Rovira i Virgili |
LIST OF PARTICIPANTS
Dan Alexandru, Universitat de Barcelona
Lluís Alsedà, Centre de Recerca Matemàtica
Joyce Aparecida, Universidade Estadual de Campinas
Alicja Barbara, Universitat Politècnica de Catalunya
Salvador Borrós, Universitat Autònoma de Barcelona
Luis Ángel Calderón, Universidad de Extremadura
Murilo R. Cândido, Universidade Estadual de Campinas
Jordi Canela, Centre de Recerca Matemàtica
Yagor R. Carvalho, Universidade Estadual Paulista
Anna Cima, Universitat Autònoma de Barcelona
Marcos Coutinho, Universidade de São Paulo
Clara Cufí-Cabré, Universitat Autònoma de Barcelona
Francisco Bruno Gomes da Silva, Universidade Estadual de Campinas
Peter De Maesschalck, Universiteit Hasselt
Kealey Dias City, University of New York
Igsyl Domínguez, Pontificia Universidad Católica de Chile
Nuria Fagella, Universitat de Barcelona
Ernest Fontich, Universitat de Barcelona
Isaac García, Universitat de Lleida
Antonio Garijo, Universitat Rovira i Virgili
Mar Giralt, Universitat Politècnica de Catalunya
Marina Gonchenko, Universitat de Barcelona
Yulij Ilyashenko, NRU – Higher School of Economics
Xavier Jarque, Universitat de Barcelona
Angel Jorba, Universitat de Barcelona
José Tomás Lázaro, Universitat Politècnica de Catalunya
Jaume Llibre, Universitat Autònoma de Barcelona
Alejandro López Freie, Universität Berlin
Khudoyor Mamayusupov, NRU – Higher School of Economics
Yohanna Paulina M. Mancilla, Universidad del Bío-Bío
Víctor Mañosa, Universitat Politècnica de Catalunya
Francesc Mañosas, Universitat Autònoma de Barcelona
Alejandro Marqués, Universidad de Sevilla
Félix Martínez, Universitat Politècnica de València
Kevin Martínez, Centre de Recerca Matemàtica
Susanna Maza, Universitat de Lleida
Beatriz Molina-Samper, Universidad de Valladolid
Román Moreno, Universitat Politècnica de Catalunya
David Jesús Nieves, Universidad Complutense de Madrid
Dmitry Novikov Weizmann, Institute of Science
Chara Pantazi, Universitat Politècnica de Catalunya
Jaime Paradela, Universitat Politècnica de Catalunya
Jordi Penalva, Universidad de las Islas Baleares
Dino Peran, Sveucilište u Splitu
Ivan Pereira, Universitat de les Illes Balears
Alfred Peris, Universitat Politècnica de València
Enrique Ponce, Universidad de Sevilla
Mario Ponce, Pontificia Universidad Católica de Chile
Ariel Reyes, Pontificia Universidad Católica de Chile
David Reyner, Universitat Politècnica de Catalunya
Ana Livia Rodero, Universidade Estadual Paulista
Miriam Romero, Universidad Autónoma del Estado de Morelos
Gabriel Alexis Rondón, Universidade Estadual de Campinas
Iván Sánchez, Universitat Autònoma de Barcelona
Paulo Henrique Reis Santana, Universidade Estadual Paulista
Fernando Sanz, Universidad de Valladolid
Mitsuhiro Shishikura, Kyoto University
Bishnu Hari Subedi, Tribhuvan University
Joan Carles Tatjer, Universitat de Barcelona
Sergi de la Torre, Universitat Politècnica de Catalunya
Joan Torregrosa, Universitat Autònoma de Barcelona
Ana Maria Travaglini, Universidade de São Paulo
Mariana Queiroz Velter, Universidade Federal de Goiás
Marcelo Viana, IMPA – Intituto de Matemática Pura e Aplicada
Enrique Vigil, Universidad de Oviedo
Jordi Villadelprat, Universitat Rovira i Virgili
Melvin Yeung, Universiteit Hasselt
INVOICE/PAYMENT INFORMATION
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LODGING INFORMATION
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For inquiries about this event please contact the Scientific Events Coordinator Ms. Núria Hernández at nhernandez@crm.cat
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