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Invariant Structures for Dynamical Systems: Poisson Dynamics by Cariñena, José F.; Ibort, Alberto; Marmo, Giuseppe; Morandi, Giuseppe is a scholarly article available to read on EtoBox.

What is Invariant Structures for Dynamical Systems: Poisson Dynamics about?

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 just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related

Author

Cariñena, José F.; Ibort, Alberto; Marmo, Giuseppe; Morandi, Giuseppe

Publisher

Springer Netherlands : Imprint : Springer

Published

2015

Language

EN

ISBN

9789401792202