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Journal of Geometric Mechanics

Open Access Articles

Martin Bauer, Martins Bruveris and Peter W. Michor
2017, 9(2): i-iii doi: 10.3934/jgm.201702i +[Abstract](818) +[HTML](602) +[PDF](31.6KB)
Pedro L. García and Manuel de León
2013, 5(4): v-vi doi: 10.3934/jgm.2013.5.4v +[Abstract](839) +[PDF](90.6KB)
This Special Issue of the Journal of Geometric Mechanics is devoted to the Proceedings of the Third Iberoamerican Meetings on Geometry, Mechanics and Control, which was held at the University of Salamanca (Spain) from September 3 until September 7, 2012.

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Juan-Pablo Ortega
2011, 3(4): ii-iv doi: 10.3934/jgm.2011.3.4ii +[Abstract](1026) +[PDF](209.6KB)
In July 2010 we celebrated the 60th birthday of Tudor S. Ratiu with a workshop entitled ``Geometry, Mechanics, and Dynamics" that was held at the Centre International de Rencontres Mathématiques in Luminy. Tudor is one of the world's most renowned and esteemed mathematicians and this conference was a great occasion to go over the numerous subjects on which he has worked and had a deep influence. Most of these topics are strongly connected to the subject matter of this journal, whose very foundation owes much to Tudor's encouragement and support.
    I coorganized this event with the late Jerry Marsden who was the main force behind it and started its preparation several years in advance as it was his habit with so many other things. Jerry was not only Tudor's PhD advisor but also his main collaborator for thirty years, friend, mentor and as for many of us, an endless source of intellectual inspiration. This is why we felt so sad when we learnt that his health had deteriorated and that he could not attend the meeting he had put so much dedication on and, needless to say, so devastated when the news of his passing arrived a few months later.

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A note on the Wehrheim-Woodward category
Alan Weinstein
2011, 3(4): 507-515 doi: 10.3934/jgm.2011.3.507 +[Abstract](1068) +[PDF](407.2KB)
Wehrheim and Woodward have shown how to embed all the canonical relations between symplectic manifolds into a category in which the composition is the usual one when transversality and embedding assumptions are satisfied. A morphism in their category is an equivalence class of composable sequences of canonical relations, with composition given by concatenation. In this note, we show that every such morphism is represented by a sequence consisting of just two relations, one of them a reduction and the other a coreduction.

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