Area-preserving diffeomorphisms from the C1-Standpoint

Bessa, Mário

http://hdl.handle.net/10400.2/13925

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Authors

Bessa, Mário

Abstract(s)

More than thirty years have passed since Newhouse (Am. J. Math. 99:1061–1087, 1977) published a dichotomy on C1 area-preserving diffeomorphisms. Here we revisit some central results on surface conservative C1-diffeomorphisms by presenting, in particular, a new proof of Newhouse’s theorem and also by proving some, although folklore, not yet proved results on this setting. We intend that this exposition can be used by a large audience as an introduction to the concept of dominated splitting and its relevance to the theory of C1-stability of area-preserving diffeomorphisms.

Keywords

Periodic orbit Lyapunov exponent Periodic point Elliptic orbit Homoclinic point

URI

http://hdl.handle.net/10400.2/13925

Citation

Bessa, M. (2011). Area-Preserving Diffeomorphisms from the C1-Standpoint. In: Peixoto, M., Pinto, A., Rand, D. (eds) Dynamics, Games and Science II. Springer Proceedings in Mathematics, vol 2. Springer, Berlin, Heidelberg