Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality. This
book is a state-of-the-art account, covering classical and new results. The volume comprises …

One-dimensional dynamics has developed in the last decades into a subject in its own right.
Yet, many recent results are inaccessible and have never been brought together. For this …

Our aim is to show that the Julia-Fatou--Sullivan structure theory for the dynamics of rational
maps is also valid for smooth endomorphisms of the circle (and of the interval) under …

Foliations is one of the major concepts of modern geometry and topology meaning a
partition of topological space into a disjoint sum of leaves. This book is devoted to geometry …

Dynamics of piecewise contractions of the interval Page 1 Ergod. Th. & Dynam. Sys. (2015),
35, 2198–2215 doi:10.1017/etds.2014.16 c Cambridge University Press, 2014 Dynamics of …

Piecewise-continuous maps consist of smooth bran-ches separated by jumps, ie isolated
discontinui-ties. They appear not to be constrained by the same rules that come with being …

В монографии обосновывается и развивается метод построения эффективных
топологических инвариантов динамических систем и слоений, у которых имеются …

A survey of works concerning a kind of generalization of the Poincaré rotation number for a
rather general class of flows on closed surfaces is given. The idea (going back to A. Weil) is …

Lorenz maps are dynamical systems on the interval related to the Lorenz flow. Monotone
Lorenz families will be introduced and it will be shown that all possible topological …

We study weakly order preserving circle maps with a flat interval, which are differentiable
even on the boundary of the flat interval. We obtain estimates on the Lebesgue measure and …