Format:
Online-Ressource (XXVI, 411 p. 119 illus., 64 illus. in color, online resource)
ISBN:
9783642388309
Series Statement:
Springer Proceedings in Mathematics & Statistics 54
Content:
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. Buic˘a, I.A. García and S.Maza: Inverse Jacobi multipliers: recent applications in dynamical systems -- J.S. Cánovas: On entropy of non–autonomous 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. Pumari˜no, 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.
Content:
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.
Note:
Description based upon print version of record
,
Foreword; Preface; Acknowledgements; Contents; List of Contributors; Secants of Trajectories in Dimension Three; 1 Introduction; 2 Morse-Smale Type Conditions; 2.1 Two-Dimensional Saddle-Connections; 2.2 Infinitesimal Saddle-Connections; 3 Poincaré-Bendixson Traps; References; Statistical Stability in Chaotic Dynamics; 1 Introduction; 2 Physical Measures; 3 Quadratic Maps; 3.1 Physical Measures; 3.2 Statistical Instability; 3.3 Statistical Stability; 4 Lorenz Flow; 4.1 Geometric Model; 4.2 Physical Measures; 4.3 Statistical Stability; 5 Contracting Lorenz Flow; 5.1 Rovella Maps
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5.2 A Final RemarkReferences; Combinatorial Dynamics and an Elementary Proof of the Continuity of the Topological Entropy at θ=101, in the Milnor Thurston World; 1 Introduction and Statements of the Results; 2 A Technical Lemma; 2.1 Maximal Neighbors Periodic Orbits; 2.2 The Permutation Map; 3 Proof of the Continuity of the Map h(θ) at θ=101; 3.1 Continuity of the Map htop(θ) at θk= H11,10k (101), k = 1, 2, 3, …; References; Homoclinic Spirals: Theory and Numerics; 1 Introduction; 2 Spiral Structures: Homoclinic Loop; 3 Homoclinic Spirals: Kneading Invariants for Lorenz Like Systems
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4 ConclusionsReferences; Numerical Results on a Simple Model for the Confinement of Saturn's F Ring; 1 Introduction; 2 A `Minimalist' Model for Saturn's F Ring; 3 Numerical Results; 4 Discussion; References; Analysis of the Full Vibrational Dynamics of the LiNC/LiCN Molecular System; 1 Introduction; 2 The LiNC/LiCN Molecular System; 3 Computational Procedure; 3.1 Trajectory Calculations and Frequency Analysis; 3.2 SALI Calculation; 4 Results and Discussion; 4.1 SALI Maps for the 2dof LiNC/LiCN Model; 4.2 SALI Maps for the Full Dimensional Vibrational Dynamics of the LiNC/LiCN Molecule
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4.3 SALI Frequency Maps5 Summary; References; Resonance and Singularities; 1 What Is Resonance?; 1.1 Periodically Driven Oscillators; 1.2 Torus Flows and Circle Mappings; 1.3 Conclusions and Examples; 2 Periodically Driven Oscillators Revisited; 2.1 Parametric Resonance; 2.2 The Hill-Schrödinger Equation; 2.3 Driven and Coupled Van der Pol-Like Oscillators; 3 Universal Studies; 3.1 The Hopf-Neĭmark-Sacker Bifurcation; 3.2 The Hopf Saddle-Node Bifurcation for Diffeomorphisms; 4 Conclusions; 4.1 `Next Cases'; 4.2 Modelling; 5 Appendix: Equivariant Singularity Theory
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5.1 Lyapunov-Schmidt Reduction5.2 Equivariant Singularity Theory; 5.3 Resonances in Forced Oscillators; References; Inverse Jacobi Multipliers: Recent Applications in Dynamical Systems; 1 Introduction; 2 Autonomous Differential Systems; 2.1 Invariant Manifolds Through Singularities; 2.2 Limit Cycles; 3 Monodromic Singularities on Center Manifolds in R3; 3.1 The Center Problem in R3; 3.2 Multiple Hopf Bifurcation in R3; 3.3 Lie Symmetries Near Monodromic Points in R3; 4 Non-autonomous Differential Systems and Non-autonomous Inverse Jacobi Multipliers
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4.1 A Nonautonomous Extension of the Darboux Construction
,
ForewordPreface -- 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. Buic˘a, I.A. García and S.Maza: Inverse Jacobi multipliers: recent applications in dynamical systems -- J.S. Cánovas: On entropy of non-autonomous 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. Pumari˜no, 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.
Additional Edition:
ISBN 9783642388293
Additional Edition:
Druckausg. Progress and challenges in dynamical systems Berlin : Springer, 2013 ISBN 9783642388293
Additional Edition:
ISBN 3642388299
Language:
English
Subjects:
Mathematics
Keywords:
Dynamisches System
;
Konferenzschrift
DOI:
10.1007/978-3-642-38830-9
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Author information:
Ibáñez, Santiago
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