Dynamics Reported: Dynamics Reported. New Series, cartea 3

en Limba Engleză Paperback – 16 dec 2011

DYNAMICS REPORTED reports on recent developments in dynamical systems. Dynamical systems of course originated from ordinary differential equations. Today, dynamical systems cover a much larger area, including dynamical processes described by functional and integral equations, by partial and stochastic differential equations, etc. Dynamical systems have involved remarkably in recent years. A wealth of new phenomena, new ideas and new techniques are proving to be of considerable interest to scientists in rather different fields. It is not surprising that thousands of publications on the theory itself and on its various applications are appearing DYNAMICS REPORTED presents carefully written articles on major subjects in dynamical systems and their applications, addressed not only to specialists but also to a broader range of readers including graduate students. Topics are advanced, while detailed exposition of ideas, restriction to typical results - rather than the most general one- and, last but not least, lucid proofs help to gain the utmost degree of clarity. It is hoped, that DYNAMICS REPORTED will be useful for those entering the field and will stimulate an exchange of ideas among those working in dynamical systems Summer 1991 Christopher K. R. T Jones Drs Kirchgraber Hans-Otto Walther Managing Editors Table of Contents Limit Relative Category and Critical Point Theory G. Fournier, D. Lupo, M. Ramos, M. Willem 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Relative Category . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3. Relative Cupiength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 6 4. Limit Relative Category . . . . . . . . . . . . . . . . . . . . . . . '" . . . . " . . . . . . . . . . . . . . . . 10 5. The Deformation Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 6. Critical Point Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 7. Some Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Specificații

ISBN-13: 9783642782367
ISBN-10: 3642782361
Pagini: 176
Ilustrații: VIII, 162 p.
Dimensiuni: 155 x 235 x 10 mm
Greutate: 0.28 kg
Ediția:Softcover reprint of the original 1st ed. 1994
Editura: Springer
Colecția Dynamics Reported. New Series
Seria Dynamics Reported. New Series

Locul publicării:Berlin, Heidelberg, Germany

Cuprins

Limit Relative Category and Critical Point Theory.- 1. Introduction.- 2. Relative Category.- 3. Relative Cuplength.- 4. Limit Relative Category.- 5. The Deformation Lemma.- 6. Critical Point Theorems.- 7. Some Applications.- 8. A Perturbation Theorem.- References.- Coexistence of Infinitely Many Stable Solutions to Reaction Diffusion Systems in the Singular Limit.- 1. Introduction and singular limit slow dynamics.- 2. Intuitive Approach to the Stability of Multi-layered Solutions.- 3. The SLEP Method for the Stability of Normal N-layered Solutions.- 4. Recovery Process of Stability.- 5. Concluding Remarks.- Appendix A.- Appendix B.- Appendix C.- References.- Recent advances in regularity of second-order hyperbolic mixed problems, and applications.- 1. Introduction.- I: Regularity Theory.- 2. Regularity under Dirichlet boundary conditions.- 3. Regularity under Neumann Boundary Conditions.- 4. Cosine/Sine (Semigroup) Representation Formulae of the Solutions.- II: Applications.- 5. Well-posedness of Semi-linear Wave Equations with Neumann Boundary Conditions.- 6. Local Exponential Stability of Damped Wave Equations with Semi-linear Boundary Conditions.- 7. Exact Controllability of Semi-linear Hyperbolic Problems.- 8. Riccati Operator Equations and Hyperbolic Mixed Problems.- References.

Textul de pe ultima copertă

This book contains four excellent contributions on topics in dynamical systems by authors with an international reputation: "Hyperbolic and Exponential Dichotomy for Dynamical Systems", "Feedback Stabilizability of Time-periodic Parabolic Equations", "Homoclinic Bifurcations with Weakly Expanding Center Manifolds" and "Homoclinic Orbits in a Four-Dimensional Model of a Perturbed NLS Equation: A Geometric Singular Perturbation Study". All the authors give a careful and readable presentation of recent research results, addressed not only to specialists but also to a broader range of readers including graduate students.