Sökning: "hyperbolic fixed points"

Hittade 4 avhandlingar innehållade orden hyperbolic fixed points.

  1. 1. Computer-aided Computation of Abelian integrals and Robust Normal Forms

    Författare :Tomas Johnson; Warwick Tucker; Lars-Erik Persson; John H. Hubbard; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Ordinary differential equations; parameter estimation; planar Hamiltonian systems; bifurcation theory; Abelian integrals; limit cycles; normal forms; hyperbolic fixed points; numerical integration; invariant manifolds; interval analysis. 2000 Mathematics Subject Classification. 34A60; 34C07; 34C20; 37D10; 37G15; 37M20; 37M99; 65G20; 65L09; 65L70.; MATHEMATICS; MATEMATIK; matematik; Mathematics;

    Sammanfattning : This PhD thesis consists of a summary and seven papers, where various applications of auto-validated computations are studied. In the first paper we describe a rigorous method to determine unknown parameters in a system of ordinary differential equations from measured data with known bounds on the noise of the measurements. LÄS MER

  3. 2. Construction of Adaptive Multistep Methods for Problems with Discontinuities, Invariants, and Constraints

    Författare :Fatemeh Mohammadi; Numerisk analys; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; multistep methods; Initialization; beta-blocking; Discontinuity; Time adaptivity; Strong stability preserving; Differential algebraic equations;

    Sammanfattning : Adaptive multistep methods have been widely used to solve initial value problems. These ordinary differential equations (ODEs) may arise from semi-discretization of time-dependent partial differential equations(PDEs) or may combine with some algebraic equations to represent a differential algebraic equations (DAEs). LÄS MER

  4. 3. Renormalization of Lorenz Maps

    Författare :Björn Winckler; Marco Martens; Michael Benedicks; Welington de Melo; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematical analysis; Analys;

    Sammanfattning : This thesis is a study of the renormalization operator on Lorenz αmaps with a critical point. Lorenz maps arise naturally as first-return maps for three-dimensional geometric Lorenz flows. Renormalization is a tool for analyzing the microscopic geometry of dynamical systems undergoing a phase transition. LÄS MER

  5. 4. Topics in Analysis and Computation of Linear Wave Propagation

    Författare :Mohammad Motamed; Olof Runborg; Shi Jin; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Numerical analysis; Numerisk analys;

    Sammanfattning : This thesis concerns the analysis and numerical simulation of wave propagation problems described by systems of linear hyperbolic partial differential equations. A major challenge in wave propagation problems is numerical simulation of high frequency waves. LÄS MER