Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems

by Wilfrid Gangbo

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Published 2010 by American Mathematical Society in Providence, R.I .
Written in

Subjects:

• Differential forms,
• Hamiltonian systems,
• Infinite-dimensional manifolds

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Edition Notes

Statement	Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini
Series	Memoirs of the American Mathematical Society -- no. 993, Memoirs of the American Mathematical Society -- no. 993.
Contributions	Kim, Hwa Kil, Pacini, Tommaso, 1971-
Classifications
LC Classifications	QA381 .G36 2010
The Physical Object
Pagination	v, 77 p. ;
Number of Pages	77
ID Numbers
Open Library	OL25053542M
ISBN 10	0821849395
ISBN 10	9780821849392
LC Control Number	2011002947
OCLC/WorldCa	701619907

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Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems. Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems He describes local and global duality in the special case of irreducible algebraic varieties of an algebraically closed base field k in terms of differential forms and their residues. Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share .

that the Hamiltonian is preserved along any solution of our evolutive system: H(µt) = H(µ0). c Wiley Periodicals, Inc. 1 Introduction In the last few years there has been a considerable interest in the theory of gra-dient flows in the Wasserstein space P2(RD) of probability measures with finite. Hamiltonian dynamics Gaetano Vilasi Textbook and monographs featuring material suitable for and based on a two-semester course on analytical mechanics, differential geometry, sympletic manifolds and integrable systems. Floer–Novikov cohomology and the flux conjecture. Differential Forms on Wasserstein Space and Infinite-Dimensional Hamiltonian Systems Methods of Morse theory are of special importance.

J. Lott In Sect. 5 we compute the Riemannian curvature of P∞(M).The answer is relatively simple. As an application, if M has sectional curvatures bounded below by r ∈ R, one can ask whether P∞(M)necessarily has sectional curvatures bounded below by turns out to be the case if and only if r = 0. There has been recent interest in doing Hamiltonian mechanics on the Wasserstein. Linear Hamiltonian systems P. Rapisarda∗ H.L. Trentelman† Abstract We study linear Hamiltonian systems using bilinear and quadratic differential forms. Such a representation-free approach allows to use the same concepts and techniques to deal with systems isolated from their environment and with systems subject to external. A one-form assigns to each vector tangent to a manifold a real number in a linear way. You may think of a vector tangent to a manifold as being determined by two points on the manifold that are "infinitesimally close", and hence view a 1-form as a function from such infinitesimal pairs of points to the real numbers.