Periodic Motions

1994. Auflage 1994
ISBN: 978-0-387-94204-9
Verlag: Springer

Buch, Englisch, Band 104, 578 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 1007 g

Reihe: Applied Mathematical Sciences

"The task is done; the Maker rests. And lo! The engine turns. A million years shall flow, Ere round its axle shall the wheel run slow And a new cog be needed. " Mad8.ch: The Tragedy of Man J.C.W. Horne's translation In this book I tried to sum up the facts and results I considered most important concerning periodic solutions of ordinary differential equations (ODEs) produced by this century from Henri Poincare up to the youngest mathematician appearing in the list of references. I have included also some results of my own that did not find their way into monographs in the past. I have done research in this direction for more than 25 years and have given graduate courses about some of the topics covered for many years at the Budapest University of Technology and also at the Universidad Central de Venezuela in Caracas. I hope that people interested in differential equations and applications may use this experience. Some may say that periodic solutions of ODEs has been a closed chapter of mathematics for some time.

Zielgruppe

Graduate

Autoren/Hrsg.

Farkas, Miklos

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Naturwissenschaften Physik Mechanik Akustik, Schwingungsanalyse
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

Inhaltsverzeichnis

1 Introduction.- 2 Periodic Solutions of Linear Systems.- 3 Autonomous Systems in the Plane.- 4 Periodic Solutions of Periodic Systems.- 5 Autonomous Systems of Arbitrary Dimension.- 6 Perturbations.- 7 Bifurcations.- Al Matrices.- A2 Topological Degree and Fixed Point Theorems.- A3 Invariant Manifolds.- References.- Symbols.