Related papers: H\'enon maps: a list of open problems

In this paper some open problems for Painlev\'e equations are discussed. In particular the following open problems are described: (i) the Painlev\'e equivalence problem; (ii) notation for solutions of the Painlev\'e equations; (iii)…

We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.

The existence of the Herman ring of a function adds interest and complexity to the dynamics of the function. We present a detailed and understandable summary of the core discoveries and recent developments on the Herman ring of rational and…

A precise meaning is given to the notion of continuous iteration of a mapping. Usual discrete iterations are extended into a dynamical flow which is a homotopy of them all. The continuous iterate reveals that a dynamical map is formend by…

We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.

This is a list of several open problems dealing mainly with univariate polynomials.

We discuss tangent maps related to the multipliers of periodic points of a typical one-dimensional polynomial map.

Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…

Many mathematicians encounter k-to-1 maps only in the study of covering maps. But, of course, k-to-1 maps do not have to be open. This paper touches on covering maps, and simple maps, but concentrates on ordinary k-to-1 functions (both…

Non-linear maps can possess various dynamical behaviors varying from stable steady states and cycles to chaotic oscillations. Most models assume that individuals within a given population are identical ignoring the fundamental role of…

The dynamics of transcendental functions in the complex plane has received a significant amount of attention. In particular much is known about the description of Fatou components. Besides the types of periodic Fatou components that can…

This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…

We present the basic formulation of Hamilton dynamics in complex phase space. We extend the Hamilton's function by including the imaginary part and find out the corresponding Hamilton's canonical equation of motion. Example of simple…

Inspired by the Erd\H{o}s' problem in Ramsey theory, we propose a dynamical version of the problem and answer it positively for circle maps.

We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…

We study dynamical systems arising from word maps on simple groups. We develop a geometric method based on the classical trace map for investigating periodic points of such systems. These results lead to a new approach to the search of…

In the theory of open quantum systems, divisibility of the system dynamical maps is related to memory effects in the dynamics. By decomposing the system Hilbert space as a direct sum of several Hilbert spaces, we study the relationship…

We collect from several sources some of the most important results on the forward and backward limits of points under real and complex rational functions, and in particular real and complex Newton maps, and we provide numerical evidence…

This work surveys the topological and statistical properties of real quadratic maps and investigates the complex quadratic maps under holomorphic and non-holomorphic singular perturbations.

In this paper, we study three relative LS categories of a map and study some of their properties. Then we introduce the `higher topological complexity' and `weak higher topological complexity' of a map. Each of them are homotopy invariants.…