Smaleova podkev

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:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[M. Žilavec]
UDC:	517.9
COBISS:	18436953
Views:	559
Downloads:	263
Average score:	0 (0 votes)
Metadata:

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