PristupačnostThe page provides a list of national and international projects where FER participates or has participated as a project coordinator or partner.
Project database
Projects
Project
Acronym:
0036031
Name:
Nonlinear analysis of differential equations and dynamical systems
Project status:
From: 2002-08-22
To: 2006-12-31
(Completed)
Type (Programme):
MZOS 2002
Croatian partner
Organisation name:
-
Contact person name:
Mervan, Pašić
Contact person tel:
6129-901
Short description of project
Already since the beginning of 20th century nonstandard methods of mathematical analysis have been developed in order to understand fractal properties of sets in Euclidean spaces. The most important fractal properties are described by various fractal dimensions, like Hausdorff dimension, box dimension, Lyapunov dimension, Renyi spectrum for dimensions, correlation dimension, information dimension, Hentschel-Procaccia spectrum for dimensions, packing dimension, and effective fractal dimension. In our research the notion of box dimension is by far the most important.
The box dimension and the related Minkowski content are of interest for understanding some qualitative properties of solutions of differential equations and dynamical systems. Indeed, box dimension of a graph of solution or a spiral trajectory can be viewed as information about its `dimensional concentration' near a given point or a limit cycle respecitvely. The Minkowski content provides us subtler information then box dimension.