Minimum Action Curves in Degenerate Finsler Metrics (häftad)

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Geometri

Format: Häftad (Paperback / softback)
Språk: Engelska
Antal sidor: 186
Utgivningsdatum: 2015-07-21
Upplaga: 1st ed. 2015
Förlag: Springer International Publishing AG
Illustratör/Fotograf: Bibliographie 1 schwarz-weiße und 11 farbige Abbildungen
Illustrationer: 11 Illustrations, color; 3 Illustrations, black and white; XV, 186 p. 14 illus., 11 illus. in color.
Dimensioner: 234 x 156 x 11 mm
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Antal komponenter: 1
Komponenter: 1 Paperback / softback
ISBN: 9783319177526

Minimum Action Curves in Degenerate Finsler Metrics

Name: Minimum Action Curves in Degenerate Finsler Metrics
Price: 411.00 SEK
Availability: InStock
Author: Matthias Heymann
ISBN: 9783319177526

Existence and Properties

av Matthias Heymann

Häftad, Engelska, 2015-07-21

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Presenting a study of geometric action functionals (i.e., non-negative functionals on the space of unparameterized oriented rectifiable curves), this monograph focuses on the subclass of those functionals whose local action is a degenerate type of Finsler metric that may vanish in certain directions, allowing for curves with positive Euclidean length but with zero action. For such functionals, criteria are developed under which there exists a minimum action curve leading from one given set to another. Then the properties of this curve are studied, and the non-existence of minimizers is established in some settings. Applied to a geometric reformulation of the quasipotential of Wentzell-Freidlin theory (a subfield of large deviation theory), these results can yield the existence and properties of maximum likelihood transition curves between two metastable states in a stochastic process with small noise. The book assumes only standard knowledge in graduate-level analysis; all higher-level mathematical concepts are introduced along the way.

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Preface.- Acknowledgements.- Acronyms.- Part I: Results.- Introduction.- Geometric Action Functionals.- Existence of Minimum Action Curves.- Properties of Minimum Action Curves.- Conclusions.- Some Proofs and Remarks.- Part II: Proofs.- Finding Points with Local Minimizers.- Proof of Lemma 6.1.- Part III: Proof of a Technical Lemma.- Proof of Lemma 6.15: Main Arguments.- Proof of Lemma 6.15: Some Technical Details.- Glossary.- Index.- References.