Takensov teorem i primjene

Živković, Karla (2015) Takensov teorem i primjene. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

At the very beginning of this paper we are introduced to some basic examples and concepts of dynamic systems. We explained different types of dynamic systems, defined orbits, types of points in the dynamic systems and introduced the concept of the attractors and some of its properties, which is very important for the understanding of the dynamic systems theory. In the second chapter we studied topological dynamic systems and their properties. We explained limit sets, minimal sets and the term of recurrence. We introduced the concepts and properties of dynamic systems regarding to being topologically transitive, expansive or topologically mixing. Furthermore, next chapter, Dimensions, treated three different definitions of dimensions (Lebesgue covering dimension, Hausdorff dimension and upper box-counting dimension) and investigated what being ’finite dimensional’ implies in terms of embeddings into Euclidean spaces for each of these definitions. In the fourth chapter we presented the main subject of this paper, the Takens theorem and its proof. We also introduce some technical results. In the last chapter we gave an important example in the dynamics theory - Lorenz equations and Lorenz attractor (defined by those equations).

Item Type: Thesis (Diploma thesis)
Supervisor: Slijepčević, Siniša
Date: 2015
Number of Pages: 43
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 29 Oct 2015 15:09
Last Modified: 29 Oct 2015 15:09
URI: http://digre.pmf.unizg.hr/id/eprint/4339

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