Lectures on Topological Fluid Mechanics
Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological f
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Lecture Notes in Mathematics
1
Mitchell A. Berger Louis H. Kauffman Boris Khesin
H. Keith Moffatt Renzo L. Ricca De Witt Sumners
Lectures on Topological Fluid Mechanics
1973 Cetraro, Italy 2001 Editor: Renzo L. Ricca
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Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1973
C.I.M.E. means Centro Internazionale Matematico Estivo, that is, International Mathematical Summer Center. Conceived in the early fifties, it was born in 1954 and made welcome by the world mathematical community where it remains in good health and spirit. Many mathematicians from all over the world have been involved in a way or another in C.I.M.E.’s activities during the past years. So they already know what the C.I.M.E. is all about. For the benefit of future potential users and cooperators the main purposes and the functioning of the Centre may be summarized as follows: every year, during the summer, Sessions (three or four as a rule) on different themes from pure and applied mathematics are offered by application to mathematicians from all countries. Each session is generally based on three or four main courses (24−30 hours over a period of 6-8 working days) held from specialists of international renown, plus a certain number of seminars. A C.I.M.E. Session, therefore, is neither a Symposium, nor just a School, but maybe a blend of both. The aim is that of bringing to the attention of younger researchers the origins, later developments, and perspectives of some branch of live mathematics. The topics of the courses are generally of international resonance and the participation of the courses cover the expertise of different countries and continents. Such combination, gave an excellent opportunity to young participants to be acquainted with the most advance research in the topics of the courses and the possibility of an interchange with the world famous specialists. The full immersion atmosphere of the courses and the daily exchange among participants are a first building brick in the edifice of international collaboration in mathematical research. C.I.M.E. Director Pietro ZECCA Dipartimento di Energetica “S. Stecco” Università di Firenze Via S. Marta, 3 50139 Florence Italy e-mail: [email protected]
C.I.M.E. Secretary Elvira MASCOLO Dipartimento di Matematica Università di Firenze viale G.B. Morgagni 67/A 50134 Florence Italy e-mail: [email protected]
For more information see CIME’s homepage: http://www.cime.unifi.it CIME’s activity is supported by: – Ministero dell’Universita’, Ricerca Scientifica e Tecnologica COFIN ’99 – Ministero degli Affari Esteri - Direzione Generale per la Promozione e la Cooperazione - Ufficio V – CNR Consiglio Nazionale delle Ricerche – E.U. under the Training and Mobility of Researchers Programme – UNESCO-ROSTE, Venice Office
Mitchell A. Berger • Louis H. Kauffman Boris Khesin • H. Keith Moffatt Renzo L. Ricca • De Witt Sumners
Lectures on Topological Fluid Mechanics Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy July 2–10, 2001
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