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 …

This is a self-contained introduction to the classical theory of homoclinic bifurcation theory,
as well as its generalizations and more recent extensions to higher dimensions. It is also …

In 438 alphabetically-arranged essays, this work provides a useful overview of the core
mathematical background for nonlinear science, as well as its applications to key problems …

In this paper we shall show that there exists a polynomial unimodal map f:[0, 1]→[0, 1] with
so-called Fibonacci dynamics which is non-renormalizable and in particular, for each x from …

In this paper geometric properties of infinitely renormalizable real Hénon-like maps F in R^ 2
are studied. It is shown that the appropriately defined renormalizations R n F converge …

This book grew out of the work developed at the University of Warwick, under the
supervision of Ian Stewart, which formed the core of my Ph. D. Thesis. Most of the results …

The appearance of numerous period-doubling cascades is among the most prominent
features of parametrized maps, that is, smooth one-parameter families of maps F: ℝ× 𝔐→ 𝔐 …

We study the phenomenon of a collision of a Hénon-like attractor with a Hénon-like repeller
leading to the emergence of mixed dynamics in the model describing the motion of two point …

We prove the uniform hyperbolicity of the near-parabolic renormalization operators acting on
an infinite-dimensional space of holomorphic transformations. This implies the universality of …

We study highly dissipative Hénon maps F_ c, b:(x, y) ↦ (cx^ 2-by, x) with zero entropy. They
form a region Π in the parameter plane bounded on the left by the curve W of infinitely …