Relations Between Dynamical Systems And Knot Theory

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Madani, Meysam | 2009

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 39799 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fanaii, Hamid Reza
Abstract:
In fact knot theory is working by an elastic string. A knot is A smooth embedding of in . We say that two knots are equivalent if there is an ambient isotopic between them. In knot theory we study equivalent classes of knots. As it seems from its name, a dynamical system is the study of motions, mechanics and dynamics of a system. We will observe some systems and stability of orbits in theme. Then we define templates which contain orbits in themselves. At last, we observe relations between discrete dynamical systems and knot theory. Then for any arbitrary chaotic knot we observe that there exist an universal template that contain a copy of any kind of not. Finally we will study some open problems which related to this subjects.
Keywords:
Textures ; Dynamical Systems ; Universal Template ; Closed Orbits

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