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.

Inhalt
Foreword.- Preface.- C. Alonso-González, F. Cano, R. Rosas: Secants of trajectories in dimension three.- J. F. Alves, M. Soufi: Statistical stability in chaotic dynamics.- S. Aranzubía and R. Labarca: Combinatorial dynamics and an elementary proof of the continuity of the topological entropy at q =101, in the Milnor Thurston World.- R. Barrio, F. Blesa, S. Serrano, T. Xing and A. Shilnikov: Homoclinic spirals: theory and numerics.- L. Benet and À. Jorba: Numerical results on a simple model for the confinement of Saturn's F Ring.- P. Benítez, J.C. Losada, R.M. Benito, and F. Borondo: Analysis of the full vibrational dynamics of the LiNC/LiCN molecular system.- H.W. Broer and G. Vegter: Resonance and Singularities.- A. Buica, I.A. García and S.Maza: Inverse Jacobi multipliers: recent applications in dynamical systems.- J.S. Cánovas: On entropy of nonautonomous discrete systems.- F. Alvaro Carnicero and F. Sanz: Interlacing and separation of solutions of linear meromorphic ODEs.- A.Chenciner: A walk through the New Methods of Celestial Mechanics.- L. J. Díaz and K. Gelfert: Porcupine-like Horseshoes. Topological and Ergodic Aspects.- E. Freire, E. Ponce and F. Torres: Planar Filippov Systems with Maximal Crossing Set and Piecewise Linear Focus Dynamics.- A. Gasull and H. Giacomini: Some applications of the extended Bendixson-Dulac Theorem.- S. Gefter and T. Stulova: On solutions of zero exponential type for some inhomogeneous differential-difference equations in a Banach space.- M. Guardia, P. Martín and T.M. Seara: Homoclinic solutions to infinity and oscillatory motions in the Restricted Planar Circular Three Body Problem.- I.S. Labouriau and A.A.P. Rodrigues : Partial symmetry breaking and heteroclinic tangencies.- M.A. Martínez, R. Barrio and S. Serrano: Finding Periodic Orbits in the Hindmarsh-Rose neuron model.- D. Peralta-Salas: Realization problems in the theory of foliations.- E. Ponce, J. Ros and E. Vela: A Hopf-zero degenerated case in symmetric piecewise linear systems.- E. Ponce, J. Ros and E. Vela: The Focus-Center-Limit Cycle Bifurcation in Discontinuous Planar Piecewise Linear Systems without Sliding.- A. Pumarino, J. A. Rodríguez, J. C. Tatjer and E. Vigil: Piecewise linear bidimensional maps as models of return maps for 3D diffeomorphisms.- C. Simó, P. Sousa-Silva and M. Terra: Practical Stability Domains near L4,5 in the Restricted Three-Body Problem: Some preliminary facts.- C. Simó and A. Vieiro: A physical dissipative system with a Poincar´e homoclinic figure-eight.- G. de la Vega and S. López de Medrano: Generalizing the May-Leonard System to any number of species.- Index.