The Theory of Singularities and Its Applications

Author: V. I. Arnold,Vladimir Igorevich Arnolʹd

Publisher: Cambridge University Press

ISBN: 9780521422802

Category: Mathematics

Page: 72

View: 7957

This book describes those singularities encountered in different branches of mathematics. The distinguished mathematician, Vladimir Arnold, avoids giving difficult proofs of all the results in order to provide the reader with a concise and accessible overview of the many guises and areas in which singularities appear. Some of these areas include geometry and optics, optimal control theory and algebraic geometry, reflection groups theory, dynamical systems theory, and the classical and quantum catastrophe theory.
Posted in Mathematics

Singularity Theory for Non-Twist KAM Tori

Author: A. González-Enríquez, A. Haro,R. de la Llave

Publisher: American Mathematical Soc.

ISBN: 0821890182

Category: Mathematics

Page: 115

View: 9942

In this monograph the authors introduce a new method to study bifurcations of KAM tori with fixed Diophantine frequency in parameter-dependent Hamiltonian systems. It is based on Singularity Theory of critical points of a real-valued function which the authors call the potential. The potential is constructed in such a way that: nondegenerate critical points of the potential correspond to twist invariant tori (i.e. with nondegenerate torsion) and degenerate critical points of the potential correspond to non-twist invariant tori. Hence, bifurcating points correspond to non-twist tori.
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Dynamical Systems V

Bifurcation Theory and Catastrophe Theory

Author: V.I. Arnold,V.S. Afrajmovich,Yu.S. Il'yashenko,L.P. Shil'nikov

Publisher: Springer Science & Business Media

ISBN: 3642578845

Category: Mathematics

Page: 274

View: 2758

Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.
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Aesthetic Computing

Author: Paul A. Fishwick

Publisher: MIT Press

ISBN: 0262562375

Category: Computers

Page: 457

View: 1286

The application of the theory and practice of art to computer science: how aesthetics and art can play a role in computing disciplines.
Posted in Computers

Catastrophe Theory

Author: Vladimir I. Arnol'd

Publisher: Springer Science & Business Media

ISBN: 9783540548119

Category: Mathematics

Page: 150

View: 6837

The new edition of this non-mathematical review of catastrophe theory contains updated results and many new or expanded topics including delayed loss of stability, shock waves, and interior scattering. Three new sections offer the history of singularity and its applications from da Vinci to today, a discussion of perestroika in terms of the theory of metamorphosis, and a list of 93 problems touching on most of the subject matter in the book.
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Solitons and Geometry

Author: S. P. Novikov,Sergeĭ Petrovich Novikov

Publisher: Cambridge University Press

ISBN: 9780521471961

Category: Mathematics

Page: 58

View: 4607

In this book, Professor Novikov describes recent developments in soliton theory and their relations to so-called Poisson geometry. This formalism, which is related to symplectic geometry, is extremely useful for the study of integrable systems that are described in terms of differential equations (ordinary or partial) and quantum field theories. Professor Novikov examines several Hamiltonian systems, within the framework of Poisson geometry, to demonstrate its power. This book will be of interest to mathematicians and physicists.
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Proceedings

Author: International Conference on Computer Vision

Publisher: N.A

ISBN: 9780780350984

Category: Computer vision

Page: 1164

View: 3092

Posted in Computer vision

Rapport

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 3744

Posted in Mathematics

Séminaire de Mathématique

Author: Denis Bonheure

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 14

View: 5284

Posted in Mathematics

Grundkurs Topologie

Author: Gerd Laures,Markus Szymik

Publisher: Springer-Verlag

ISBN: 3662459531

Category: Mathematics

Page: 242

View: 2781

Die Topologie beschäftigt sich mit den qualitativen Eigenschaften geometrischer Objekte. Ihr Begriffsapparat ist so mächtig, dass kaum eine mathematische Struktur nicht mit Gewinn topologisiert wurde. Dieses Buch versteht sich als Brücke von den einführenden Vorlesungen der Analysis und Linearen Algebra zu den fortgeschrittenen Vorlesungen der Algebraischen und Geometrischen Topologie. Es eignet sich besonders für Studierende in einem Bachelor- oder Masterstudiengang der Mathematik, kann aber auch zum Selbststudium für mathematisch interessierte Naturwissenschaftler dienen. Die Autoren legen besonderen Wert auf eine moderne Sprache, welche die vorgestellten Ideen vereinheitlicht und damit erleichtert. Definitionen werden stets mit vielen Beispielen unterlegt und neue Konzepte werden mit zahlreichen Bildern illustriert. Über 170 Übungsaufgaben (mit Lösungen zu ausgewählten Aufgaben auf der Website zum Buch) helfen, die vermittelten Inhalte einzuüben und zu vertiefen. Viele Abschnitte werden ergänzt durch kurze Einblicke in weiterführende Themen, die einen Ausgangspunkt für Studienarbeiten oder Seminarthemen bieten. Neben dem üblichen Stoff zur mengentheoretischen Topologie, der Theorie der Fundamentalgruppen und der Überlagerungen werden auch Bündel, Garben und simpliziale Methoden angesprochen, welche heute zu den Grundbegriffen der Geometrie und Topologie gehören.
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Analysis II

Author: Christiane Tretter

Publisher: Springer-Verlag

ISBN: 3034804768

Category: Mathematics

Page: 149

View: 3409

Das Lehrbuch ist der zweite von zwei einführenden Bänden in die Analysis. Es zeichnet sich dadurch aus, dass alle Themen der Analysis 2 kompakt zusammengefasst sind und dennoch auf typische Schwierigkeiten eingegangen wird. Beginnend mit der Topologie metrischer Räume über die Differentialrechnung von Funktionen mehrerer reeller Variablen bis zu gewöhnlichen Differentialgleichungen und Fourierreihen, enthält das Buch alle prüfungsrelevanten Inhalte. Der Stoff kann anhand von Beispielen, Gegenbeispielen und Aufgaben nachvollzogen werden.
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Kreis und Kugel

Author: Wilhelm Blaschke

Publisher: Walter de Gruyter

ISBN: 3111506932

Category: Mathematics

Page: 175

View: 5735

Posted in Mathematics