Periodic points of symmetric product mappings

Fixed Points of Symmetric Product Mappings

Fixed Point Indices and Periodic Points of Holomorphic Mappings

Let ∆ be the ball |x| < 1 in the complex vector space C, let f : ∆ → C be a holomorphic mapping and let M be a positive integer. Assume that the origin 0 = (0, . . . , 0) is an isolated fixed point of both f and the M -th iteration f of f . Then for each factor m of M, the origin is again an isolated fixed point of f and the fixed point index μfm(0) of f m at the origin is well defined, and so ...

A Note on the Shadowing Lemma and Symmetric Periodic Points

A standard use of shadowing lemmas in dynamical systems theory is to prove density of periodic points. When there is symmetry present it is natural to investigate the density of periodic points of a given symmetry. We obtain several results in this direction. As an application, we prove a result about compact group extensions of hyperbolic and nonuniformly hyperbolic dynamical systems.

Fixed Points, Periodic Points, and Coin-tossing Sequences for Mappings Defined on Two-dimensional Cells

We propose, in the general setting of topological spaces, a definition of two-dimensional oriented cell and consider maps which possess a property of stretching along the paths with respect to oriented cells. For these maps, we prove some theorems on the existence of fixed points, periodic points, and sequences of iterates which are chaotic in a suitable manner. Our results, motivated by the st...

Approximating fixed points of generalized nonexpansive mappings