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A Fatou-Julia decomposition of transversally holomorphic foliations

Taro Asuke (2010)

Annales de l’institut Fourier

A Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one was given by Ghys, Gomez-Mont and Saludes. In this paper, we propose another decomposition in terms of normal families. Two decompositions have common properties as well as certain differences. It will be shown that the Fatou sets in our sense always contain the Fatou sets in the sense of Ghys, Gomez-Mont and Saludes and the inclusion is strict in some examples. This property is important when discussing...

An introduction to loopoids

Janusz Grabowski (2016)

Commentationes Mathematicae Universitatis Carolinae

We discuss a concept of loopoid as a non-associative generalization of Brandt groupoid. We introduce and study also an interesting class of more general objects which we call semiloopoids. A differential version of loopoids is intended as a framework for Lagrangian discrete mechanics.

Area functionals and Godbillon-Vey cocycles

Takashi Tsuboi (1992)

Annales de l'institut Fourier

We investigate the natural domain of definition of the Godbillon-Vey 2- dimensional cohomology class of the group of diffeomorphisms of the circle. We introduce the notion of area functionals on a space of functions on the circle, we give a sufficiently large space of functions with nontrivial area functional and we give a sufficiently large group of Lipschitz homeomorphisms of the circle where the Godbillon-Vey class is defined.

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