Overview
- Provides interdisciplinary geometric models in differential geometry, analytical mechanics, dynamical systems, electrodynamics, economics, and theoretical and mathematical physics
- Structured in two parts to present both the geometrical theory and the applicative models
- Studies the differential geometry of spaces in which the metric used for measuring changes in function of time and momentum
Part of the book series: Synthesis Lectures on Mathematics & Statistics (SLMS)
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Table of contents (8 chapters)
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Front Matter
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Time-Dependent Hamilton Geometry
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Front Matter
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Applications to Dynamical Systems, Economy and Theoretical Physics
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Front Matter
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Back Matter
Keywords
About this book
This book studies a category of mathematical objects called Hamiltonians, which are dependent on both time and momenta. The authors address the development of the distinguished geometrization on dual 1-jet spaces for time-dependent Hamiltonians, in contrast with the time-independent variant on cotangent bundles. Two parts are presented to include both geometrical theory and the applicative models: Part One: Time-dependent Hamilton Geometry and Part Two: Applications to Dynamical Systems, Economy and Theoretical Physics. The authors present 1-jet spaces and their duals as appropriate fundamental ambient mathematical spaces used to model classical and quantum field theories. In addition, the authors present dual jet Hamilton geometry as a distinct metrical approach to various interdisciplinary problems.
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Authors and Affiliations
About the authors
Mircea Neagu, Ph.D., is an Associate Professor in the Department of Mathematics and Computer Science at the Transylvania University of Brasov. He received his Ph.D. in mathematics from the Polytechnic University of Bucharest.
Alexandru Oană, Ph.D., is a Lecturer in the Department of Mathematics and Computer Science at the Transylvania University of Brasov. He received his B.S. in mathematics followed by his Ph.D. in differential geometry dependent on higher order accelerations.Bibliographic Information
Book Title: Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications
Authors: Mircea Neagu, Alexandru Oană
Series Title: Synthesis Lectures on Mathematics & Statistics
DOI: https://doi.org/10.1007/978-3-031-08885-8
Publisher: Springer Cham
eBook Packages: Synthesis Collection of Technology (R0), eBColl Synthesis Collection 11
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-08884-1Published: 01 September 2022
Softcover ISBN: 978-3-031-08887-2Published: 02 September 2023
eBook ISBN: 978-3-031-08885-8Published: 31 August 2022
Series ISSN: 1938-1743
Series E-ISSN: 1938-1751
Edition Number: 1
Number of Pages: XII, 87
Number of Illustrations: 1 b/w illustrations
Topics: Differential Geometry, Mathematical Physics, Dynamical Systems and Ergodic Theory, Vibration, Dynamical Systems, Control, Complexity, Classical Electrodynamics