Detaljer för kursplan för kurs FMFN05F giltig från och med Spring 2019 Utskriftsvänlig visning Kurskod:FMFN05F Gäller från och med:Spring 2019 Kursplanen är fastställd Allmänt Undervisningsspråk:English Ges:Varje vårtermin Kurshemsida:http://www.matfys.lth.se/education/FMFN05/ Syfte 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. Innehåll 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. Kunskap och förståelse För godkänd kurs skall doktoranden have a general knowledge about system conditions leading to chaotic and regular behaviour, respectively. be familiar with mathematical methods used to analyse chaotic systems. have a general understanding why it is useful to introduce dimensions which are not integer. Färdighet och förmåga För godkänd kurs skall doktoranden be able to apply mathematical methods used for the description of non-linear systems. be able to analyse the time development of a system and be able to determine if the system is chaotic or regular. be able to determine which mathematical models are appropriate in different situations. be able to determine the dimension of simple fractals. Värderingsförmåga och förhållningssätt För godkänd kurs skall doktoranden Undervisningsformer Föreläsningar Laborationer Projekt Examinationsformer Skriftlig tentamen Skriftlig rapport Kommentarer: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 Förkunskapskrav Förutsatta förkunskaper Elementary mathematics and mechanics. Multivariate calculus and elementary partial differential equations. Urvalskriterier Litteratur Litteratur:Ohlén, G., Åberg, S. & Östborn, P.: Chaos, Compendium. Lund 2006.. Lund, 2006.Strogatz, S. H.: Nonlinear dynamics and Chaos. Westview Press. ISBN 9780813349107. Övrig information Kurskod Kurskod:FMFN05F Administrativ information Datum för fastställande: -05-26 Beslutad av:Anders Gustafsson FTF-AGU Alla publicerade kurstillfällen för kursplanen Inga matchande kurstillfällen hittades. 0 kurstillfällen. Utskriftsvänlig visning