Madrid, 23 January 2023 - 27 January 2023

PRESENTATION

madrid

This is the 19th RTNS (Recent Trends in Nonlinear Science) winter school in Dynamical Systems of the DANCE (Dinámica, Atractores y Nolinealidad: Caos y Estabilidad) Spanish network. We will start a new format with only two courses of 10 hours each. During afternoons, some of the participants will have the opportunity to present their recent works as short talks.

The RTNS2023 will take place at ICMAT in Madrid (Cantoblanco Campus).


SPONSORS

logo_MCI  logo_ICMAT

COMMITTEES

COORDINATORS

Joan Torregrosa (Universitat Autònoma de Barcelona)
Patricia Yanguas (Universidad Pública de Navarra)

SCIENTIFIC COMMITTEE

María Jesús Álvarez Torres (Universitat de les Illes Balears)
Rosa María Benito Zafrilla (Universidad Politécnica de Madrid)
Gérard Iooss (Université de Nice)


ORGANIZING COMMITTEE

Francisco Javier Arranz Saiz (Universidad Politécnica de Madrid)
Florentino Borondo Rodríguez  (Universidad Autónoma de Madrid - ICMAT)
Laia Domingo Colomer (Universidad Autónoma de Madrid - ICMAT)
Juan Carlos Losada González (Universidad Politécnica de Madrid)
Mar Grande Toledano (Universidad Politécnica de Madrid)
Fabio Revuelta Peña (Universidad Politécnica de Madrid)
Alberto Vergel Otero (Universidad Politécnica de Madrid - ICMAT)

 

schedule

SHORT TALKS 

Session I:

  1. Numerical computation of regularities of invariant objects with Daubechies wavelets
    Salvador Borrós Cullell (Universitat Autònoma de Barcelona, Spain)
  2. Local niteness of limit cycles for perturbations of linear non-degenerated centers in R3
    María Martín Vega (Universidad de Valladolid, Spain)
  3. Nilpotent centers on center manifolds in R3
    Lucas Queiroz Arakaki (São Paulo State University, Brazil)
  4. Relationship of the Green's functions related to the Hill's equation coupled to different boundary value conditions
    Mouhcine Yousfi (Universidade de Santiago de Compostela, Spain)

Session II:

  1. On a population model with density dependence and Allee effect
    Jose S. Cánovas (Universidad Politécnica de Cartagena, Spain)
  2. Flow map parameterization method for whiskered tori in quasi-periodic Hamiltonian systems
    Álvaro Fernández Mora (Universitat de Barcelona, Spain)
  3. Interaction between Hopf bifurcations in neuron models
    Diego Noriega Rodríguez (Universidad de Oviedo, Spain)

Session III:

  1. Poincaré-Hopf theorem for Filippov vector fields and Filippov singularity indices
    Joyce Aparecida Casimiro (State University of Campinas, Brazil)
  2. Critical transitions on nonautonomous d-concave population models
    Jesús Dueñas Pamplona (Universidad de Valladolid, Spain)
  3. Chaos and integrability from geometrodynamics
    Alberto Vergel Otero (Universidad Politécnica de Madrid-ICMAT, Spain)

Session IV:

  1. Higher order analysis in non-Lipschitz differential equations for periodic solutions using topological degree
    Francisco Bruno Gomes da Silva (State University of Campinas, Brazil)
  2. Limit cycles of some new families of phi-Laplacian Liénard equations
    Set Pérez Gonzalez (Universidad de Oviedo, Spain)
  3. Applications of the invariant manifolds in Chemistry
    Fabio Revuelta (Universidad Politécnica de Madrid, Spain)
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We will introduce several tools to study the number of limit cycles for families of ordinary differential equations (ODE), paying special attention on planar polynomial ODE and on one-dimensional periodic non-autonomous ones. These are the main subjects of the course:

  1. Poincaré map and local study of periodic orbits. Bifurcations of codimension one of limit cycles. Algebraic limit cycles.
  2. A miscellanea of useful tools: Chebyshev systems, rational parameterizations, Poincaré-Miranda theorem, Resultants.
  3. Upper bounds for the number of limit cycles: Lyapunov and Bendixson-Dulac approaches.
  4. Lower bounds for the number of limit cycles: Lyapunov constants, Abelian integrals and algebraic solutions.
  5. Abel type differential equations.
 A Journey in Nonlinear Dynamics Riding Optical Waves - Mariana Haragus (Institut FEMTO-ST, Université de Franche-Comté, France)

Starting from the mathematical questions raised by a problem in nonlinear optics, we present several tools used in the study of nonlinear waves. Focusing on bifurcations and stability, we discuss:

  1. The Lugiato-Lefever equation and its mathematical questions.
  2. Some elementary local bifurcations.
  3. Center manifolds and normal forms.
  4. Spatial dynamics and bifurcations of steady waves.
  5. Nonlinear dynamics of periodic waves.
 Clementa Alonso González, Universidad de Alicante (Spain)
 Joyce Aparecida Casimiro, Universidade Estadual de Campinas (Brazil)
 Francisco Javier Arranz, Universidad Politécnica de Madrid (Spain)
 Miquel Barcelona Poza, Universitat Autònoma de Barcelona (Spain)
 Rosa M. Benito, Universidad Politécnica de Madrid (Spain)
 Florentino Borondo, Universidad Autónoma de Madrid (Spain)
 Salvador Borrós Cullell, Universitat Autònoma de Barcelona (Spain)
 Luis Ángel Calderón Pérez, Universitat de les Illes Balears (Spain)
 Jose S. Cánovas, Universidad Politécnica de Cartagena (Spain)
 Jesús Dueñas Pamplona, Universidad de Valladolid (Spain)
 Marina Esteban, Universidad de Córdoba (Spain)
 Álvaro  Fernández Mora, Universitat de Barcelona (Spain)
 Fernando Fernández Sánchez, Universidad de Sevilla (Spain)
 Lluc Manuel Ferré Escobet, Universitat Autònoma de Barcelona (Spain)
 Isaac  García, Universitat de Lleida (Spain)
 Armengol Gasull, Universitat Autònoma de Barcelona (Spain)
 Francisco Bruno Gomes da Silva, Universidade Estadual de Campinas (Brazil)
 Mariana Haragus, Université de Franche-Comté (France)
 Víctor  Lanchares Barrasa, Universidad de La Rioja  (Spain)
 Ernesto Lanchares Sánchez, Universidad de La Rioja (Spain)
 Juan Carlos Losada, Universidad Politécnica de Madrid (Spain)
 María Martín Vega, Universidad de Valladolid (Spain)
 Susanna Maza, Universitat de Lleida (Spain)
 Mónica Molina Becerra, Universidad de Sevilla (Spain)
 Juan José Morales Ruiz, Universidad Politécnica de Madrid (Spain)
 Ainoa Murillo López, Universitat de Barcelona (Spain)
 Diego Noriega Rodríguez, Universidad de Oviedo (Spain)
 Set Pérez González, Universidad de Oviedo (Spain)
 Enrique Ponce Núñez, Universidad de Sevilla (Spain)
 Lucas Queiroz Arakaki, Universidade Estadual Paulista (Brazil)
 Fabio Revuelta, Universidad Politécnica de Madrid (Spain)
 Fernando Sanz Sánchez, Universidad de Valladolid (Spain)
 Juan R. Sisternes Alacot, Universidad Politécnica de Madrid (Spain)
 Joan Torregrosa, Universitat Autònoma de Barcelona (Spain)
 Carles Trullàs Fernàndez, Universitat Politècnica de Catalunya (Spain)
 Alberto Vergel, Universidad Politécnica de Madrid (Spain)
 Arturo Vieiro Yanes, Universitat de Barcelona (Spain)
 Mouhcine Yousfi, Universidade de Santiago de Compostela (Spain)
 Javier Ros Padilla, Universidad de Sevilla (Spain)
 Elísabet Vela Felardo, Universidad de Córdoba  (Spain)
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