Wyniki wyszukiwania - BazTech

1

On fractal dimension estimation

Pánek D., Kropik P., Predota A.

Przegląd Elektrotechniczny

|

2011

|

R. 87, nr 5

120-122

EN

The paper deals with an algorithm for Hausdorff dimension estimation based on box-counting dimension calculation. The main goal of the paper is to propose a new approach to box-counting dimension calculation with less computational demands.

PL

W artykule opisano algorytm estymacji wymiaru Hausdorffa oparty o wyznaczanie wymiaru pudełkowego. Głównym celem pracy jest zaproponowanie nowego podejścia do wyznaczania wymiaru pudełkowego, które ma znacznie mniejszą złożoność obliczeniową.

2

O wymiarze wykresu funkcji nigdzie nieróżniczkowalnej

Szarek T.

Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne

|

2006

|

[Z] 42

15-20

3

On the hyperbolic Hausdorff dimension of the boundary of a basin of attraction for a holomorphic map and of quasirepellers

Przytycki F.

Bulletin of the Polish Academy of Sciences. Mathematics

|

2006

|

Vol. 54, no 1

41-52

EN

We prove that the hyperbolic Hausdorff dimension of Fr Ω, the boundary of the simply connected immediate basin of attraction Ω to an attracting periodic point of a rational mapping of the Riemann sphere, which is not a finite Blaschke product in some holomorphic coordinates, or a 2 : 1 factor of a Blaschke product, is larger than 1. We prove a "local version" of this theorem, for a boundary repelling to the side of the domain. The results extend an analogous fact for polynomials proved by A. Zdunik and relies on the theory elaborated by M. Urbanski, A. Zdunik and the author in the late 80-ties. To prove that the dimension is larger than 1, we use expanding repellers in δΩ constructed in [P2]. To reach our results, we deal with a quasi-repeller, i.e. the limit set for a geometric coding tree, and prove that the hyperbolic Hausdorff dimension of the limit set is larger than the Hausdorff dimension of the projection via the tree of any Gibbs measure for a Holder potential on the shift space, under a non-cohomology assumption. We also consider Gibbs measures for Holder potentials on Julia sets.

4

On a dimension of measures

Lasota A., Myjak J.

Bulletin of the Polish Academy of Sciences. Mathematics

|

2002

|

Vol. 50, no 2

221-235

EN

Using the notion of the Levy concentration function we discuss a definition of the dimension for probability measures. This dimension is strongly connected with the correlation dimension of measures and with the Hausdorff dimension of sets. Moreover, we calculate some bounds of this dimension for measures generated by Iterated Function Systems and by a partial differential equation.

5

Chaos deterministyczny i atraktory w procesach dynamicznych

Terlikowski T.

Przegląd Geofizyczny

|

2000

|

Z. 3-4

279-288

EN

In this paper the basic notions of the s.c. deterministic chaos concept are briefly collected and dis-cussed. Some methods commonly known and used of a chaotic dynamics reconstruction on the base of given time series are presented (the embedding approach). The methods are applied to determine the basic parameters of the attractor of a dynamic process; namely the embedding dimension, the correlation and topological dimension of the attractor, as well as its Lapunov exponent (a measure of instability). The identification of the process nature and es-timation of its parameters is necessary before undertaking an attempt to determine a prediction model for a process representing deterministic chaos.