New topological invariants for real- and angle-valued maps: an alternative to Morse–Novikov theory
"This book is about new topological invariants of real- and angle-valued maps inspired by Morse–Novikov theory, a chapter of topology, which has recently raised interest outside of mathematics; for example, in data analysis, shape recognition, computer science and physics. They are the backbone...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Publishing Co. Pte Ltd.
© 2018
|
| Schlagworte: | |
| Online-Zugang: | FHN01 URL des Erstveroeffentlichers |
| Zusammenfassung: | "This book is about new topological invariants of real- and angle-valued maps inspired by Morse–Novikov theory, a chapter of topology, which has recently raised interest outside of mathematics; for example, in data analysis, shape recognition, computer science and physics. They are the backbone of what the author proposes as a computational alternative to Morse–Novikov theory, referred to in this book as AMN-theory. These invariants are on one side analogues of rest points, instantons and closed trajectories of vector fields and on the other side, refine basic topological invariants like homology and monodromy. They are associated to tame maps, considerably more general than Morse maps, that are defined on spaces which are considerably more general than manifolds. They are computable by computer implementable algorithms and have strong robustness properties. They relate the dynamics of flows that admit the map as "Lyapunov map" to the topology of the underlying space, in a similar manner as Morse–Novikov theory does."--Publisher's website |
| Beschreibung: | Title from PDF title page (viewed September 7, 2017) |
| Beschreibung: | 1 online resource (259 p.) ill |
| ISBN: | 9789814618250 |
Internformat
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Datensatz im Suchindex
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| author | Burghelea, Dan |
| author_facet | Burghelea, Dan |
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| id | DE-604.BV044640455 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:58Z |
| institution | BVB |
| isbn | 9789814618250 |
| language | English |
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| physical | 1 online resource (259 p.) ill |
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| spelling | Burghelea, Dan Verfasser aut New topological invariants for real- and angle-valued maps an alternative to Morse–Novikov theory by Dan Burghelea Singapore World Scientific Publishing Co. Pte Ltd. © 2018 1 online resource (259 p.) ill txt rdacontent c rdamedia cr rdacarrier Title from PDF title page (viewed September 7, 2017) "This book is about new topological invariants of real- and angle-valued maps inspired by Morse–Novikov theory, a chapter of topology, which has recently raised interest outside of mathematics; for example, in data analysis, shape recognition, computer science and physics. They are the backbone of what the author proposes as a computational alternative to Morse–Novikov theory, referred to in this book as AMN-theory. These invariants are on one side analogues of rest points, instantons and closed trajectories of vector fields and on the other side, refine basic topological invariants like homology and monodromy. They are associated to tame maps, considerably more general than Morse maps, that are defined on spaces which are considerably more general than manifolds. They are computable by computer implementable algorithms and have strong robustness properties. They relate the dynamics of flows that admit the map as "Lyapunov map" to the topology of the underlying space, in a similar manner as Morse–Novikov theory does."--Publisher's website Manifolds (Mathematics) Mappings (Mathematics) Topological spaces Electronic books http://www.worldscientific.com/worldscibooks/10.1142/9254#t=toc Verlag URL des Erstveroeffentlichers Volltext |
| spellingShingle | Burghelea, Dan New topological invariants for real- and angle-valued maps an alternative to Morse–Novikov theory Manifolds (Mathematics) Mappings (Mathematics) Topological spaces Electronic books |
| title | New topological invariants for real- and angle-valued maps an alternative to Morse–Novikov theory |
| title_auth | New topological invariants for real- and angle-valued maps an alternative to Morse–Novikov theory |
| title_exact_search | New topological invariants for real- and angle-valued maps an alternative to Morse–Novikov theory |
| title_full | New topological invariants for real- and angle-valued maps an alternative to Morse–Novikov theory by Dan Burghelea |
| title_fullStr | New topological invariants for real- and angle-valued maps an alternative to Morse–Novikov theory by Dan Burghelea |
| title_full_unstemmed | New topological invariants for real- and angle-valued maps an alternative to Morse–Novikov theory by Dan Burghelea |
| title_short | New topological invariants for real- and angle-valued maps |
| title_sort | new topological invariants for real and angle valued maps an alternative to morse novikov theory |
| title_sub | an alternative to Morse–Novikov theory |
| topic | Manifolds (Mathematics) Mappings (Mathematics) Topological spaces Electronic books |
| topic_facet | Manifolds (Mathematics) Mappings (Mathematics) Topological spaces Electronic books |
| url | http://www.worldscientific.com/worldscibooks/10.1142/9254#t=toc |
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