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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/26213

Title: Grassmann Dynamics
Authors: Morfin Ramírez, Mario Leonardo
Advisor: Shub, Michael
Pugh, Charles Chapman
Department: Mathematics
Keywords: Real Dynamical Systems
Issue Date: 17-Feb-2011
Abstract: The present work is divided in two parts. The first is concerned with the dynamics on the Grassmann manifold of k-dimensional subvector spaces of an n dimensional real or complex vector space induced by a linear invertible transformation A of the vector space into itself. The Grassmann map GA sends p to Ap, and one asks, what are the dynamics of GA? In the second part, I consider dynamics induced by a linear cocycle covering a diffeomorphism of a compact manifold, acting on the Grassmann bundle of k-dimensional linear subspaces of TN. I prove a Kupka-Smale theorem for the space of cocycles covering diffeomorphisms of a compact manifold. The proof of this theorem implies the same type of results for derived cocycles parametrized in the space of diffeomorphisms. The results of the second part can be generalized without effort to cocycles covering endomorphisms of N.
URI: http://hdl.handle.net/1807/26213
Appears in Collections:Doctoral

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