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1	Numerical analysis of random dynamical systems in the context of ship stability Julitz, David 26 August 2004 (has links) (PDF) We introduce numerical methods for the analysis of random dynamical systems. The subdivision and the continuation algorithm are powerful tools which will be demonstrated for a system from ship dynamics. With our software package we are able to show that the well known safe basin is a moving fractal set. We will also give a numerical approximation of the attracting invariant set (which contains a local attractor) and its evolution. bifurcations capsizing random attractors random dynamical system random unstable manifold ddc:510
2	A numerical case study about bifurcations of a local attractor in a simple capsizing model Julitz, David 07 October 2005 (has links) (PDF) In this article we investigate a pitchfork bifurcation of the local attractor of a simple capsizing model proposed by Thompson. Although this is a very simple system it has a very complicate dynamic. We try to reveal some properties of this dynamic with modern numerical methods. For this reason we approximate stable and unstable manifolds which connect the steady states to obtain a complete understanding of the topology in the phase space. We also consider approximations of the Lyapunov Exponents (resp. Floquet Exponents) which indicates the pitchfork bifurcation. local attractor local bifurcation numerical simulation random dynamical system unstable manifold ddc:510 Simulation Zufälliges dynamisches System
3	Numerical analysis of random dynamical systems in the context of ship stability Julitz, David 26 August 2004 (has links) We introduce numerical methods for the analysis of random dynamical systems. The subdivision and the continuation algorithm are powerful tools which will be demonstrated for a system from ship dynamics. With our software package we are able to show that the well known safe basin is a moving fractal set. We will also give a numerical approximation of the attracting invariant set (which contains a local attractor) and its evolution. info:eu-repo/classification/ddc/510 ddc:510 bifurcations capsizing random attractors random dynamical system random unstable manifold
4	A numerical case study about bifurcations of a local attractor in a simple capsizing model Julitz, David 07 October 2005 (has links) In this article we investigate a pitchfork bifurcation of the local attractor of a simple capsizing model proposed by Thompson. Although this is a very simple system it has a very complicate dynamic. We try to reveal some properties of this dynamic with modern numerical methods. For this reason we approximate stable and unstable manifolds which connect the steady states to obtain a complete understanding of the topology in the phase space. We also consider approximations of the Lyapunov Exponents (resp. Floquet Exponents) which indicates the pitchfork bifurcation. info:eu-repo/classification/ddc/510 ddc:510 Simulation Zufälliges dynamisches System local attractor local bifurcation numerical simulation random dynamical system unstable manifold
5	Complexes de type Morse et leurs équivalences Morin, Audrey 04 1900 (has links) L'obtention de ce mémoire a été rendue possible par le soutien financier du FRQNT et du CRSNG. / Ce mémoire est une étude détaillée de certains aspects de la théorie de Morse et des complexes de chaînes qui en découlent : le complexe de Morse, le complexe de Milnor et le complexe de Barraud-Cornea. À l’aide de différentes techniques de la topologie différentielle et de la théorie de Morse, dont les bases forment les premiers chapitres de ce texte, nous ferons la construction détaillée de ces trois complexes avant de démontrer leurs équivalences deux à deux. Ce mémoire synthétise et met en parallèle trois branches de la théorie de Morse en ne supposant que des connaissances du niveau d’un étudiant de début maîtrise. / In this thesis, we study aspects of Morse theory and the chain complexes that derive from it : the Morse complex, the Milnor complex and the Barraud-Cornea complex. Using different techniques from differential topology and Morse theory, which will be presented in the first chapters, we carefully build these complexes before proving their equivalence. This thesis synthesises and compares three points of view in Morse theory in a document accessible to beginning graduate students. Théorie de Morse Complexe de Morse Points critiques CW-complexes Variété connectante Éclatement d'une variété instable Morse theory Morse complex Critical points CW-complexes Connecting manifold Blow-up of the unstable manifold
6	Feigenbaum Scaling Sendrowski, Janek January 2020 (has links) In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. A more intricate approach drawing from renormalization theory as well as a short consideration of some of the topological properties will also be presented. I was furthermore trying to put great emphasis on diagrams throughout the text to make the contents more comprehensible and intuitive. Feigenbaum Feigenbaum constant Feigenbaum point superstable self-similarity fractals final-state diagram logistic map period-doubling operator linearized period-doubling operator Cantor set Sharkovsky sequence Chebyshev interpolation stable manifold unstable manifold orbits fixed points scaling factor pitchfork bifurcation cobweb plot renormalization iterates one-hump map unimodal map bifurcation cascade Feigenbaum universality chaos theory spectrum generalized Feigenvalues bifurcation points superstable points fixed function universal function eigenvalues eigenvectors eigenfunctions universality conditions Schwarzian derivative Newton’s method power method Arnoldi’s method attractive fixed point repellent fixed point Banach fixed-point theorem collocation method functional analysis topology Mathematical Analysis Matematisk analys Other Mathematics Annan matematik Computational Mathematics Beräkningsmatematik

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