:The author of this volume defines a diffusion flow for a variational problem lacking completeness related to the geometry of a contact form a a and a vector field u in its kernel. He analyzes the ends of the flow lines and finds them to be of two types: one involving periodic orbits of the Reeb (Hamiltonian) vector field x, and the other where asymptotes occur. In the most general case these turn out to be periodic motions for x up to quantic jumps of a very special type along u. He shows that the mathematical results and the physical interpretation fit and provide new points of view useful in the foundations of quantum mechanics.
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Introduction
Technical Construction of a Diffusion Flow and Convergence Theorems
The Variational Problem at Infinity
The Underlying Variational Space
The Classical Periodic Motions
Appendix 1: Some Technical Justifications
Appendix 2: The Dynamics of a (see symbol) along v (see symbol): Basic Computations
Appendix 3: Some Additional Remarks About the Physical Interpretation, Two Mathematical Conjectures
Appendix 4: How to Take Care of the Problem of the Small Normals
References
Book by Bahri Abbas
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