delo diplomskega seminarja
Mojca Žilavec (Author), Uroš Kuzman (Mentor)

Abstract

V svojem diplomskem delu sem raziskovala dinamični sistem preslikave, ki se imenuje Smaleova podkev. Le-ta je podana s preprostim predpisom, ki pravokotniku v ravnini priredi lik podkvaste oblike, vendar pa je njena dinamika izrazito kaotična. Natančneje, izkaže se, da je kaotična že njena skrčitev na del orbit, ki se začnejo v Cantorjevi podmnožici začetnega pravokotnika in in in jih opišemo s prostorom zaporedij (simbolično dinamiko). Smaleovo podkev sem uporabila tudi za raziskovanje pojava homoklinske zanke - trasverzalnega preseka stabilne in nestabilne mnogoterosti v planarnih dinamičnih sistemih.

Keywords

matematika;homoklinska zanka;kaotični sistem;podkvasta preslikava;stabilna mnogoterost;nestabilna mnogoterost;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [M. Žilavec]
UDC: 517.9
COBISS: 18436953 Link will open in a new window
Views: 559
Downloads: 263
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Other data

Secondary language: English
Secondary title: Horseshoe map
Secondary abstract: In my dissertation I have studied a discrete dynamic system given by a map, called the Smale Horseshoe map. The latter is determined by a simple rule, which tranforms a rectangle into a subtler shape and admits an extremely chaotic dynamic behaviour. More precisely, it turns out that this system is chaotic already when we restrict our attention to a part of orbits, which begin in a Cantor set of the initial rectangle and can be described with a space of sequences (symbolic dynamics). I used Smale's Horseshoe map also to explore an appearance of a homoclinic tangle - transversal intersection of the stable and unstable manifold.
Secondary keywords: mathematics;homoclinic tangle;chaotic system;horseshoe map;stable manifold;unstable manifold;
Type (COBISS): Final seminar paper
Study programme: 0
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages: 25 str.
ID: 10959920
Recommended works:
, delo diplomskega seminarja
, doctoral dissertation
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