Minimum Action Curves in Degenerate Finsler Metrics

Existence and Properties

Nonfiction, Science & Nature, Mathematics, Geometry, Statistics
Cover of the book Minimum Action Curves in Degenerate Finsler Metrics by Matthias Heymann, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Matthias Heymann ISBN: 9783319177533
Publisher: Springer International Publishing Publication: July 8, 2015
Imprint: Springer Language: English
Author: Matthias Heymann
ISBN: 9783319177533
Publisher: Springer International Publishing
Publication: July 8, 2015
Imprint: Springer
Language: English

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.

 

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

 

More books from Springer International Publishing

Cover of the book The Science of Lay Theories by Matthias Heymann
Cover of the book Public Art and Urban Memorials in Berlin by Matthias Heymann
Cover of the book Imaging the Messier Objects Remotely from Your Laptop by Matthias Heymann
Cover of the book Seasonal Adjustment Methods and Real Time Trend-Cycle Estimation by Matthias Heymann
Cover of the book Educational Equality and International Students by Matthias Heymann
Cover of the book Graphical Simulation of Deformable Models by Matthias Heymann
Cover of the book Applied Interdisciplinarity in Scholar Practitioner Programs by Matthias Heymann
Cover of the book Enterprise, Business-Process and Information Systems Modeling by Matthias Heymann
Cover of the book Underwater Robots by Matthias Heymann
Cover of the book Current Trends in Friction Stir Welding (FSW) and Friction Stir Spot Welding (FSSW) by Matthias Heymann
Cover of the book Formal Methods for Multicore Programming by Matthias Heymann
Cover of the book Digestible Quantum Field Theory by Matthias Heymann
Cover of the book Personalized Medicine with a Nanochemistry Twist by Matthias Heymann
Cover of the book Advances and Applications in Chaotic Systems by Matthias Heymann
Cover of the book Wireless Algorithms, Systems, and Applications by Matthias Heymann
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy