Displaying similar documents to “Fixed points for positive permutation braids”

Applications of Nielsen theory to dynamics

Boju Jiang (1999)

Banach Center Publications


In this talk, we shall look at the application of Nielsen theory to certain questions concerning the "homotopy minimum" or "homotopy stability" of periodic orbits under deformations of the dynamical system. These applications are mainly to the dynamics of surface homeomorphisms, where the geometry and algebra involved are both accessible.

On the ∗-product in kneading theory

Karen Brucks, R. Galeeva, P. Mumbrú, D. Rockmore, Charles Tresser (1997)

Fundamenta Mathematicae


We discuss a generalization of the *-product in kneading theory to maps with an arbitrary finite number of turning points. This is based on an investigation of the factorization of permutations into products of permutations with some special properties relevant for dynamics on the unit interval.

On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits

Roman Srzednicki (2015)

Annales Mathematicae Silesianae


We announce a new result on determining the Conley index of the Poincaré map for a time-periodic non-autonomous ordinary differential equation. The index is computed using some singular cycles related to an index pair of a small-step discretization of the equation. We indicate how the result can be applied to computer-assisted proofs of the existence of bounded and periodic solutions. We provide also some comments on computer-assisted proving in dynamics.