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  • Thesis

  • Authors: McCarthy, Anne E. (2006)

  • This thesis investigates dynamical properties of actions of abelian-by-cyclic groups on compact manifolds. For a non-singular integer matrix A, let FA be the fundamental group of the mapping cylinder of the induced map fA on the torus T n. The standard actions p), of FA on the circle RP 1 are generated by maps f(x) = Ax and gi(x) = x + bi, where A is a real-valued eigenvalue for A, and (01, ..., 0n) is the associated eigenvector. It is known that any analytic action of FA on the circle is a ramified lift of one of the standard actions p),. This thesis shows that for each analytic action, p, there exists R > 2 such that p is Cr locally rigid for all r > R. We then consider actions of the groups FA on compact manifolds of higher dimension that are generated by C1 diffeomorphisms clos...