For piecewise-smooth maps, new dynamics can be created by varying parameters such that
a fixed point collides with a surface on which the map is nonsmooth. If the map is continuous …

The main purpose of the present survey is to contribute to the theory of dynamical systems
defined by one-dimensional piecewise monotone maps. We recall some definitions known …

We recall three well-known theorems related to the simplest codimension-one bifurcations
occurring in discrete time dynamical systems, such as the fold, flip and Neimark–Sacker …

The goal of the present paper is to collect the results related to dynamics of a one-
dimensional piecewise linear map widely known as the skew tent map. These results may …

As mathematics is applied to model ever new problems in engineering and the life sciences,
increasing use is being made of systems that switch between different sets of equations on …

An asset pricing model with chartists, fundamentalists and trend followers is considered. A
market maker adjusts the asset price in the direction of the excess demand at the end of …

When nondegenerate homoclinic orbits to an expanding fixed point of a map f: X→ X, X⊆ R
n, exist, the point is called a snap-back repeller. It is known that the relevance of a snap-back …

In this paper, the character of the normal form map in the neighbourhood of a grazing orbit is
investigated for four possible configurations of soft impacting systems. It is shown that, if the …

We consider a two-parametric family of one-dimensional piecewise smooth maps with one
discontinuity point. The bifurcation structures in a parameter plane of the map are …

We develop a financial market model with interacting chartists and fundamentalists that
embeds the famous bull and bear market model of Huang and Day as a special case. Their …