Related papers: Basic Topological Structure of Fast Basins
In this paper, we investigate geometric properties of monotone systems by studying their isostables and basins of attraction. Isostables are boundaries of specific forward-invariant sets defined by the so-called Koopman operator, which…
In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read-Bajraktarevi\'{c} operators. By exhibiting a generalized "taxi-cab" metric, we show that the graph of…
We characterize when a compact, invariant, asymptotically stable attractor on a locally compact Hausdorff space is a strong deformation retract of its domain of attraction.
We study the (newtonian) gravitational force distribution arising from a fractal set of sources. We show that, in the case of real structures in finite samples, an important role is played by morphological properties and finite size…
We consider iterated functions systems (IFS) on compact metric spaces and introduce the concept of target sets. Such sets have very rich dynamical properties and play a similar role as semifractals introduced by Lasota and Myjak do for…
Euclidean triangles and IFS fractals seem to be disparate geometrical concepts, unless we consider the Sierpi\'{n}ski gasket, which is a self-similar collection of triangles. The "circumcircle" hints at a direct link, as it can be derived…
The non extensive aspects of $p_T$ distributions obtained in high energy collisions are discussed in relation to possible fractal structure in hadrons, in the sense of the thermofractal structure recently introduced. The evidences of…
Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of randomly oriented and placed deterministic fractal structures are studied theoretically. In the standard analysis, a very few parameters can be determined from SAS…
We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, point-like topological excitations, and sub-extensive topological degeneracy. We demonstrate a…
Fractal is an intriguing geometry with self-similarity and non-integer dimensions, the elastic-wave topological phase based on fractal structures has not been revealed up to now. In this work, elastic-wave higher-order topological states in…
We provide a general framework to construct fractal interpolation surfaces (FISs) for a prescribed countably infinite data set on a rectangular grid. Using this as a crucial tool, we obtain a parameterized family of bivariate fractal…
We generalize the Hyperbolic Fracton Model from the $\{5,4\}$ tessellation to generic tessellations, and investigate its core properties: subsystem symmetries, fracton mobility, and holographic correspondence. While the model on the…
We study in this paper global properties, mainly of topological nature, of attractors of discrete dynamical systems. We consider the Andronov-Hopf bifurcation for homeomorphisms of the plane and establish some robustness properties for…
In the present work, the notion of Super Fractal Interpolation Function (SFIF) is introduced for finer simulation of the objects of the nature or outcomes of scientific experiments that reveal one or more structures embedded in to another.…
We investigate the geometry of the critical fluctuations for a general system undergoing a thermal second order phase transition. Adopting a generalized effective action for the local description of the fluctuations of the order parameter…
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…
The universal fractality of river networks is very well known, however understanding of the underlying mechanisms for them is still lacking in terms of stochastic processes. By introducing probability changing dynamically, we have described…
Iterated Graph Systems (IGS) transplant ideas from fractal geometry into graph theory. Building on this framework, we extend Edge IGS from the primitive to the reducible setting. Within this broader context, we formulate rigorous…
We construct small-amplitude steady periodic gravity water waves arising as the free surface of water flows that contain stagnation points and possess a discontinuous distribution of vorticity in the sense that the flows consist of two…
The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…