Geometry from Dynamics, Classical and Quantum

• Main Authors: Cariñena, José F. (Author), Ibort, Alberto (Author), Marmo, Giuseppe (Author), Morandi, Giuseppe (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands : Imprint: Springer, 2015.
• Subjects: Physics.; Differential geometry.; Mathematical physics.; Mechanics.; Statistical physics.; Dynamical systems.; Theoretical, Mathematical and Computational Physics.; Mathematical Physics.; Statistical Physics, Dynamical Systems and Complexity.; Differential Geometry.

This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is...

Table of Contents:

• Contents
• Foreword
• Some examples of linear and nonlinear physical systems and their dynamical equations
• The language of geometry and dynamical systems: the linearity paradigm
• The geometrization of dynamical systems
• Invariant structures for dynamical systems: Poisson and Jacobi dynamics
• The classical formulations of dynamics of Hamilton and Lagrange
• The geometry of Hermitean spaces: quantum evolution
• Folding and unfolding Classical and Quantum systems
• Integrable and superintegrable systems
• Lie-Scheffers systems
• Appendices
• Bibliography
• Index.