Related papers: Abstract basins of attraction
An exterior space is a topological space provided with a quasi-filter of open subsets (closed by finite intersections). In this work, we analyze some relations between the notion of an exterior space and the notion of a discrete semi-flow.…
Diffuse scattering is usually associated with some disorder in the analyzed material. Different kinds of disorder may produce different diffuse scattering -- or not. In this letter, we demonstrate some aspects of the variety of diffuse…
In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties.…
In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…
We study whether the basin of attraction of a sequence of automorphisms of $\mathbb{C}^k$ is biholomorphic to $\mathbb{C}^k$. In particular we show that given any sequence of automorphisms with the same attracting fixed point, the basin is…
In this article we revisit the concept of abstraction as it is used in visualization and put it on a solid formal footing. While the term \emph{abstraction} is utilized in many scientific disciplines, arts, as well as everyday life,…
In this note we advocate the notion of variety as juxtaposed to the notion of complexity. Laminar flows are complex, turbulence is various. When the gradients reach a critical point, laminar flows are subjected to instabilities and…
We define an abstract setting to treat wave equations equipped with time-dependent acoustic boundary conditions on bounded domains of ${\bf R}^n$. We prove a well-posedness result and develop a spectral theory which also allows to prove a…
Passive dynamic walking is a useful model for investigating the mechanical functions of the body that produce energy-efficient walking. The basin of attraction is very small and thin, and it has a fractal-like shape; this explains the…
In this paper, we address the problem of change in an abstract argumentation system. We focus on a particular change: the addition of a new argument which interacts with previous arguments. We study the impact of such an addition on the…
At low Reynolds numbers, the hydrodynamic interaction between dumbbells driven by an external rotating field can be attractive or repulsive. Dumbbells of dissimilar asymmetric shape or different coupling to the external field undergo…
We define fractal continuations and the fast basin of the IFS and investigate which properties they inherit from the attractor. Some illustrated examples are provided.
This thesis attempts to contribute to the study of differentiable dynamics both from a semi-local and global point of view. The center of study is differentiable dynamics in manifolds of dimension 3 where we are interested in the…
We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces. We use the well-known family of NK landscapes as an example. In our case the inherent…
One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique…
In this expository article, we survey the rapidly emerging area of random geometric simplicial complexes.
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.
The planar equilateral restricted four-body problem where two of the primaries have equal masses is used in order to determine the Newton-Raphson basins of convergence associated with the equilibrium points. The parametric variation of the…
Wave packet scattering off an attractive well is investigated in two spatial dimensions numerically. The results confirm what was found previously for the one dimensional case. The wave scattered at large angles is a polychotomous (multiple…
Over the recent twenty years, argumentation has received considerable attention in the fields of knowledge representation, reasoning, and multi-agent systems. However, argumentation in dynamic multi-agent systems encounters the problem of…