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Progress and Challenges in Dynamical Systems

Proceedings of the International Conference Dynamical Systems: 100 Years after Poincaré, September 2012, Gijón, Spain

  • Conference proceedings
  • © 2013

Overview

Editors:
  1. Santiago Ibáñez

    1. Department of Mathematics, University of Oviedo, Oviedo, Spain

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  2. Jesús S. Pérez del Río

    1. Department of Mathematics, University of Oviedo, Oviedo, Spain

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  3. Antonio Pumariño

    1. Department of Mathematics, University of Oviedo, Oviedo, Spain

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  4. J. Ángel Rodríguez

    1. Department of Mathematics, University of Oviedo, Oviedo, Spain

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  • Features papers based on talks given at the International Conference Dynamical Systems: 100 years after Poincaré held at the University of Oviedo, Gijón in Spain, September 2012
  • Provides an overview of the state of the art in the study of dynamical systems that places readers at the frontiers of current knowledge in the discipline
  • Details recent advances and new trends in the field, including applications to a wide range of disciplines such as biology, chemistry, physics and economics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 54)

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Table of contents (25 papers)

  1. Front Matter

    Pages i-xxvi
    Download chapter PDF

  2. Secants of Trajectories in Dimension Three

    • C. Alonso-González, F. Cano, R. Rosas
    Pages 1-6

  3. Statistical Stability in Chaotic Dynamics

    • J. F. Alves, M. Soufi
    Pages 7-24

  4. Combinatorial Dynamics and an Elementary Proof of the Continuity of the Topological Entropy at θ =101, in the Milnor Thurston World

    • Solange Aranzubía, Rafael Labarca
    Pages 25-52

  5. Homoclinic Spirals: Theory and Numerics

    • Roberto Barrio, Fernando Blesa, Sergio Serrano, Tingli Xing, Andrey Shilnikov
    Pages 53-64

  6. Numerical Results on a Simple Model for the Confinement of Saturn’s F Ring

    • Luis Benet, Àngel Jorba
    Pages 65-75

  7. Analysis of the Full Vibrational Dynamics of the LiNC/LiCN Molecular System

    • P. Benítez, J. C. Losada, R. M. Benito, F. Borondo
    Pages 77-88

  8. Resonance and Singularities

    • Henk W. Broer, Gert Vegter
    Pages 89-126

  9. Inverse Jacobi Multipliers: Recent Applications in Dynamical Systems

    • Adriana Buică, Isaac A. García, Susanna Maza
    Pages 127-141

  10. On Entropy of Non–autonomous Discrete Systems

    • Jose S. Cánovas
    Pages 143-159

  11. Interlacing and Separation of Solutions of Linear Meromorphic ODEs

    • Félix Álvaro Carnicero, Fernando Sanz
    Pages 161-181

  12. A Walk Through the New Methods of Celestial Mechanics

    • Alain Chenciner
    Pages 183-197

  13. Porcupine-Like Horseshoes: Topological and Ergodic Aspects

    • L. J. Díaz, K. Gelfert
    Pages 199-219

  14. Planar Filippov Systems with Maximal Crossing Set and Piecewise Linear Focus Dynamics

    • Emilio Freire, Enrique Ponce, Francisco Torres
    Pages 221-232

  15. Some Applications of the Extended Bendixson-Dulac Theorem

    • Armengol Gasull, Hector Giacomini
    Pages 233-252

  16. On Solutions of Zero Exponential Type for Some Inhomogeneous Differential-Difference Equations in a Banach Space

    • Sergey Gefter, Tetyana Stulova
    Pages 253-263

  17. Homoclinic Solutions to Infinity and Oscillatory Motions in the Restricted Planar Circular Three Body Problem

    • Marcel Guardia, Pau Martín, Tere M. Seara
    Pages 265-280

  18. Partial Symmetry Breaking and Heteroclinic Tangencies

    • Isabel S. Labouriau, Alexandre A. P. Rodrigues
    Pages 281-299

  19. Finding Periodic Orbits in the Hindmarsh-Rose Neuron Model

    • M. Angeles Martínez, Roberto Barrio, Sergio Serrano
    Pages 301-308

  20. Realization Problems in the Theory of Foliations

    • Daniel Peralta-Salas
    Pages 309-323
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Keywords

About this book

This book contains papers based on talks given at the International Conference Dynamical Systems: 100 years after Poincaré held at the University of Oviedo, Gijón in Spain, September 2012. It provides an overview of the state of the art in the study of dynamical systems.

 

This book covers a broad range of topics, focusing on discrete and continuous dynamical systems, bifurcation theory, celestial mechanics, delay difference and differential equations, Hamiltonian systems and also the classic challenges in planar vector fields. It also details recent advances and new trends in the field, including applications to a wide range of disciplines such as biology, chemistry, physics and economics. 

 

The memory of Henri Poincaré, who laid the foundations of the subject, inspired this exploration of dynamical systems. In honor of this remarkable mathematician, theoretical physicist, engineer and philosopher, the authors have made a special effort to place the reader at the frontiers of current knowledge in the discipline.

Editors and Affiliations

  • Department of Mathematics, University of Oviedo, Oviedo, Spain

    Santiago Ibáñez, Jesús S. Pérez del Río, Antonio Pumariño, J. Ángel Rodríguez

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