Iterated function systems have been most extensively studied when the functions are affine transformations of Euclidean space and, more recently, projective transformations on real projective space.

In this paper, for iterated function systems, we define the classic concept of the dynamical systems: topological conjugacy of diffeomorphisms. We generalize the Hartman-Grobman theorem for ...

Fractal interpolation functions (FIFs) represent an innovative class of methods for modelling and approximating complex data. Derived from iterated function systems, these functions enable the ...

Arithmetic dynamics investigates the behaviour of iterated functions—often polynomials or rational maps—over number fields and function fields, while Galois theory provides the framework to analyse ...