Stochastics, Algebra and Analysis in Classical and Quantum Dynamics

1. Front Matter

   Pages i-xv

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2. White Noise and Stochastic Analysis

   • J. Asch, J. Potthoff

   Pages 1-14

3. Quelques Remarques sur le Cut-Locus Sous-Riemannien

   • G. Ben Arous, R. Léandre

   Pages 15-22

4. Simulation on Random Graphs of the Epidemic Dynamics of Sexually Transmitted Diseases — A New Model for the Epidemiology of AIDS

   • Georg F. Bolz

   Pages 23-51

5. Sur une Version a Deux Dimensions du Modele de Ginzburg et Landau pour la Supraconductivite

   • A. Boutet de Monvel-Berthier

   Pages 53-61

6. Differential Calculus and Integration by Parts on Poisson Space

   • Eric A. Carlen, Etienne Pardoux

   Pages 63-73

7. Introduction to Entire Cyclic Cohomology (of ℤ/2-Graded Banach Algebras)

   • Daniel Kastler

   Pages 75-152

8. Stochastic Analysis, Mathematical Structures and Distributions Methods

   • Paul Kree

   Pages 153-168

9. Ward Identities for Conformal Models

   • S. Lazzarini, R. Stora

   Pages 169-172

10. Dynamical Systems in Plasma Theory

    • E. K. Maschke

    Pages 173-187

11. Bosonic Strings and Measures on Infinite Dimensional Manifolds

    • S. Paycha

    Pages 189-203

12. A Reaction-Diffusion Model for Moderately Interacting Particles

    • H. Rost

    Pages 205-209

13. Nondegeneracy in the Perturbation Theory of Integrable Dynamical Systems

    • Helmut Rüssmann

    Pages 211-223

14. Energy Forms in Terms of White Noise

    • Ludwig Streit

    Pages 225-233

15. Linear Stability and the Parameter Modulation Approach for Solitary Waves in Hamiltonian Systems with Symmetries

    • Joachim Stubbe

    Pages 235-246

16. Back Matter

    Pages 247-247

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'Et moi, "'f si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aile':' human race. It has put common sense back Jules Verne where it belongs, 011 the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be able to do something with it. Eric T. Bell o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics . . . '; 'One service logic has rendered com­ puter science . . . '; 'One service category theory has rendered mathematics . . . '. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series_ This series, Mathematics and Its Applications, started in 1977. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope. At the time I wrote ''Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches.

• Parameter
• diffusion
• dynamical systems
• mathematical physics
• stochastics
• topology

• Fachbereich Mathematik, Ruhr-Universität, Bochum, Germany

  S. Albeverio

• BiBoS, Germany

  S. Albeverio, Ph. Blanchard

• Fakultät für Physik, Universität Bielefeld, Germany

  Ph. Blanchard

• Centre de Physique Theorique, CNRS-Luminy, Marseille, France

  D. Testard

• University of Aix-Marseille, France

  D. Testard

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