Gäller från och med: Spring 2019
Beslutad av: Anders Gustafsson FTF-AGU
Datum för fastställande: 2019-05-26
Avdelning: Mathematical Physics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: FMFN05
Undervisningsspråk: English
The course aims at giving an introduction to chaotic systems, i.e. non-linear systems that are deterministic but with a time development which is not predictable over longer periods. The course should give a possibility to reflect over the fascinating phenomena which may show up in chaotic systems, e.g. strange attractors and in this context a basic comprehension of the importance of fractal geometry, or the posibility that the solar system is instable over a longer time scale.
Kunskap och förståelse
För godkänd kurs skall doktoranden
Färdighet och förmåga
För godkänd kurs skall doktoranden
Temporally discrete systems. Feigenbaum’s theory of branching. Dependence on initial values. Fractal geometry with various applications. Different definitons of dimensions Dissipative systems. Systems of differential equations. Phase space and the Poincaré section. Lyapunov exponents and strange attractors. Coupled oscillators and frequency locking. Conservative systems and the KAM theory. Hamilton's formalism, integrable systems, billiards, area-preserving maps, chaotic motion in the solar system.
Undervisningsformer: Föreläsningar, laborationer, projekt
Examinationsformer: Skriftlig tentamen, skriftlig rapport.
Demonstrate competences in a written exam and presentation of a project. Compulsory computer exercise.
The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.
Betygsskala: Underkänd, godkänd
Examinator:
Förutsatta förkunskaper: Elementary mathematics and mechanics. Multivariate calculus and elementary partial differential equations.
Kursansvariga:
Hemsida: http://www.matfys.lth.se/education/FMFN05/