Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications

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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. Provides interdisciplinary geometric models in differential geometry, analytical mechanics, dynamical systems, electrodynamics, economics, and theoretical and mathematical physicsStructured in two parts to present both the geometrical theory and the applicative modelsStudies the differential geometry of spaces in which the metric used for measuring changes in function of time and momentum