Differential geometry applied to dynamical systems:
This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory - or the flow - may be anal...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
c2009
|
| Schriftenreihe: | World scientific series on nonlinear science. Series A.
v. 66 |
| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory - or the flow - may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes). In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem |
| Beschreibung: | xxvii, 312 p. ill. (some col.) |
| ISBN: | 9789814277150 |
Internformat
MARC
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| 520 | |a This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory - or the flow - may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes). In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem | ||
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| id | DE-604.BV044637749 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:57:51Z |
| institution | BVB |
| isbn | 9789814277150 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030035721 |
| oclc_num | 1012729594 |
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| physical | xxvii, 312 p. ill. (some col.) |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | World Scientific |
| record_format | marc |
| series2 | World scientific series on nonlinear science. Series A. |
| spelling | Ginoux, Jean-Marc Verfasser aut Differential geometry applied to dynamical systems Jean-Marc Ginoux Singapore World Scientific c2009 xxvii, 312 p. ill. (some col.) txt rdacontent c rdamedia cr rdacarrier World scientific series on nonlinear science. Series A. v. 66 This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory - or the flow - may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes). In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem Dynamics Geometry, Differential Erscheint auch als Druck-Ausgabe 9789814277143 Erscheint auch als Druck-Ausgabe 9814277142 http://www.worldscientific.com/worldscibooks/10.1142/7333#t=toc Verlag URL des Erstveroeffentlichers Volltext |
| spellingShingle | Ginoux, Jean-Marc Differential geometry applied to dynamical systems Dynamics Geometry, Differential |
| title | Differential geometry applied to dynamical systems |
| title_auth | Differential geometry applied to dynamical systems |
| title_exact_search | Differential geometry applied to dynamical systems |
| title_full | Differential geometry applied to dynamical systems Jean-Marc Ginoux |
| title_fullStr | Differential geometry applied to dynamical systems Jean-Marc Ginoux |
| title_full_unstemmed | Differential geometry applied to dynamical systems Jean-Marc Ginoux |
| title_short | Differential geometry applied to dynamical systems |
| title_sort | differential geometry applied to dynamical systems |
| topic | Dynamics Geometry, Differential |
| topic_facet | Dynamics Geometry, Differential |
| url | http://www.worldscientific.com/worldscibooks/10.1142/7333#t=toc |
| work_keys_str_mv | AT ginouxjeanmarc differentialgeometryappliedtodynamicalsystems |