By Malcolm R. Adams, Maarten Bergvelt (auth.), Tudor Ratiu (eds.)

ISBN-10: 1461397251

ISBN-13: 9781461397250

ISBN-10: 1461397278

ISBN-13: 9781461397274

The papers during this quantity are an outgrowth of the lectures and casual discussions that came about in the course of the workshop on "The Geometry of Hamiltonian platforms" which used to be held at MSRl from June five to sixteen, 1989. It used to be, in a few feel, the final significant occasion of the year-long application on Symplectic Geometry and Mechanics. The emphasis of the entire talks used to be on Hamiltonian dynamics and its courting to a number of elements of symplectic geometry and topology, mechanics, and dynamical structures normally. The organizers of the convention have been R. Devaney (co-chairman), H. Flaschka (co-chairman), ok. Meyer, and T. Ratiu. the complete assembly used to be equipped round mini-courses of 5 lectures each one and a chain of 2 expository lectures. the 1st of the mini-courses used to be given via A. T. Fomenko, who provided the paintings of his crew at Moscow college at the class of integrable platforms. the second one mini path was once given by way of J. Marsden of UC Berkeley, who spoke approximately a number of functions of symplectic and Poisson relief to difficulties in balance, general kinds, and symmetric Hamiltonian bifurcation conception. ultimately, the 2 expository talks got by way of A. Fathi of the collage of Florida who focused on the hyperlinks among symplectic geometry, dynamical structures, and Teichmiiller theory.

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**Additional info for The Geometry of Hamiltonian Systems: Proceedings of a Workshop Held June 5–16, 1989**

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Mn . They collide elastically with each other and the bottom particle collides with the floor q = o. , they fall down. Between collisions the motion of the particles is governed by the Hamiltonian where qi are the positions and Pi = mivi the momenta of the particles, i = 1, ... ,n. , 0 :::; ql :::; q2 :::; ... :::; qn and at the moment of a collision qi = qi+b 1 :::; i :::; n - 1, of i-th and i + 1 particles there is an instantaneous change of momenta (1) pi = 'YiPi + (1 + 'Yi)P;:"l Pi+l = (1 - 'Yi)pi - 'YiP;:" 1 , where 'Yi = ::~::+~, the superscript - denotes the momenta before the collision and the superscript + the momenta after the collision.

34 (1981), 259-272. 16. S. Ruijsenaars and H. Schneider, A new class of integrable systems and its relation to solitons, Ann. Phys. (NY) 170 (1986), 370-405. 17. M. Toda, "Theory of Nonlinear Lattices," Springer-Verlag, Berlin, New York, 1989. Department of Mathematics University of Pennsylvania Philadelphia, PA 19104-6395 A Universal Reduction Procedure for Hamiltonian Group Actions JUDITH M. ARMS, RICHARD H. CUSHMAN, AND MARK J. GOTAY ABSTRACT. We give a universal method of inducing a Poisson structure on a singular reduced space from the Poisson structure on the orbit space for the group action.

The Hamiltonian Hopf bifurcation", Lect. , 1160, Springer Verlag, New York, 1985. 10. , On resonant Hamiltonian systems with finitely many degrees of freedom, Lect. , 252, (1986), 19-31. 11. , Realizations of the reduced phase space of a Hamiltonian system with symmetry, Lect. , 252, (1986), 32-39. 12. , Spaces of solutions of relativistic field theories with constraints, Lect. , 987, (1982), 29-43. 13. , Symmetry and solution set singularities in Hamiltonian field theories, Acta Phys. , B17, (1986), 499-523 14.

### The Geometry of Hamiltonian Systems: Proceedings of a Workshop Held June 5–16, 1989 by Malcolm R. Adams, Maarten Bergvelt (auth.), Tudor Ratiu (eds.)

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