Related papers: Around the boundary of complex dynamics
Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…
Contents: 1. Quasiconformal Surgery and Deformations: Ben Bielefeld, Questions in quasiconformal surgery; Curt McMullen, Rational maps and Teichm\"uller space; John Milnor, Thurston's algorithm without critical finiteness; Mary Rees, A…
The study of algebraic properties of groups of transformations of a manifold gives rise to an interplay between different areas of mathemathics such as topology, geometry, and dynamical systems. Especially, in this paper, we point out some…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
We analyze the quantum dynamics of a non-relativistic particle moving in a bounded domain of physical space, when the boundary conditions are rapidly changed. In general, this yields new boundary conditions, via a dynamical composition law…
We present an approach over arbitrary fields to bound the degree of intersection of families of varieties in terms of how these concentrate on algebraic sets of smaller codimension. This provides in particular a substantial extension of the…
This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate…
We study two recent conjectures for holographic complexity: the complexity=action conjecture and the complexity=volume conjecture. In particular, we examine the structure of the UV divergences appearing in these quantities, and show that…
We investigate the dynamics of semigroups generated by a family of polynomial maps on the Riemann sphere such that the postcritical set in the complex plane is bounded. The Julia set of such a semigroup may not be connected in general. We…
The abstract boundary uses sets of curves with the bounded parameter property (b.p.p.) to classify the elements of the abstract boundary into regular points, singular points, points at infinity and so on. To study how the classification…
We wish to investigate some elementary problems concerning topological dynamics revolving around our proposed definition of escaping set. We also discuss the notion of escaping set in the induced dynamics of the hyperspace. Moreover, we…
We study the topology of the boundary manifold of a line arrangement in CP^2, with emphasis on the fundamental group G and associated invariants. We determine the Alexander polynomial Delta(G), and more generally, the twisted Alexander…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
In holomorphic semigroup dynamics, Julia set is in general backward invariant and so some fundamental results of classical complex dynamics can not be generalized to semigroup dynamics. In this paper, we define completely invariant Julia…
An increasingly important area of interest for mathematicians is the study of Abelian differentials. This growing interest can be attributed to the interdisciplinary role this subject plays in modern mathematics, as various problems of…
These notes loosely follow an introductory course on graph complexes, held at Humboldt-Universit\"at zu Berlin in summer 23. Instead of simply typing up my lecture notes I decided to give here an overview over (parts of) the topic (lecture…
Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will…
In this article, we consider hyperbolic rational maps restricted on thier Julia sets and study about the recurrence rate of typical orbits in arbitrarily small neighbourhoods around them and their relationship to the Hausdorff dimension of…