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Bifurcation without parameters

Liebscher, Stefan.

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Bifurcation without parameters

Record Type:	Electronic resources : Monograph/item
Title/Author:	Bifurcation without parameters/ by Stefan Liebscher.
Author:	Liebscher, Stefan.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xii, 142 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	Introduction -- Methods & Concepts -- Cosymmetries -- Codimension One -- Transcritical Bifurcation -- Poincar'e-Andronov-Hopf Bifurcation -- Application: Decoupling in Networks -- Application: Oscillatory Profiles -- Codimension Two -- egenerate Transcritical Bifurcation -- egenerate Andronov-Hopf Bifurcation -- Bogdanov-Takens Bifurcation -- Zero-Hopf Bifurcation -- Double-Hopf Bifurcation -- Application: Cosmological Models -- Application: Planar Fluid Flow -- Beyond Codimension Two -- Codimension-One Manifolds of Equilibria -- Summary & Outlook.
Contained By:	Springer eBooks
Subject:	Bifurcation theory. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-10777-6
ISBN:	9783319107776 (electronic bk.)

Bifurcation without parameters
Liebscher, Stefan.

Bifurcation without parameters[electronic resource] /by Stefan Liebscher. - Cham :Springer International Publishing :2015. - xii, 142 p. :ill. (some col.), digital ;24 cm. - Lecture notes in mathematics,21170075-8434 ;. - Lecture notes in mathematics ;2046..

Introduction -- Methods & Concepts -- Cosymmetries -- Codimension One -- Transcritical Bifurcation -- Poincar'e-Andronov-Hopf Bifurcation -- Application: Decoupling in Networks -- Application: Oscillatory Profiles -- Codimension Two -- egenerate Transcritical Bifurcation -- egenerate Andronov-Hopf Bifurcation -- Bogdanov-Takens Bifurcation -- Zero-Hopf Bifurcation -- Double-Hopf Bifurcation -- Application: Cosmological Models -- Application: Planar Fluid Flow -- Beyond Codimension Two -- Codimension-One Manifolds of Equilibria -- Summary & Outlook.

Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points.

ISBN: 9783319107776 (electronic bk.)

Standard No.: 10.1007/978-3-319-10777-6doiSubjects--Topical Terms:

544229
Bifurcation theory.

LC Class. No.: QA380

Dewey Class. No.: 515.392

Bifurcation without parameters
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100 1 $a Liebscher, Stefan. $3 2109642
245 1 0 $a Bifurcation without parameters $h [electronic resource] / $c by Stefan Liebscher.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xii, 142 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2117
505 0 $a Introduction -- Methods & Concepts -- Cosymmetries -- Codimension One -- Transcritical Bifurcation -- Poincar'e-Andronov-Hopf Bifurcation -- Application: Decoupling in Networks -- Application: Oscillatory Profiles -- Codimension Two -- egenerate Transcritical Bifurcation -- egenerate Andronov-Hopf Bifurcation -- Bogdanov-Takens Bifurcation -- Zero-Hopf Bifurcation -- Double-Hopf Bifurcation -- Application: Cosmological Models -- Application: Planar Fluid Flow -- Beyond Codimension Two -- Codimension-One Manifolds of Equilibria -- Summary & Outlook.
520 $a Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form calculations will help the reader to appreciate the presentation. Bifurcations without parameters occur along manifolds of equilibria, at points where normal hyperbolicity of the manifold is violated. The general theory, illustrated by many applications, aims at a geometric understanding of the local dynamics near the bifurcation points.
650 0 $a Bifurcation theory. $3 544229
650 0 $a Manifolds (Mathematics) $3 612607
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Ordinary Differential Equations. $3 891264
650 2 4 $a Partial Differential Equations. $3 890899
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 891276
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Lecture notes in mathematics ; $v 2046. $3 1534285
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-10777-6
950 $a Mathematics and Statistics (Springer-11649)