Sökning: "Warwick Tucker"

Visar resultat 1 - 5 av 8 avhandlingar innehållade orden Warwick Tucker.

  1. 1. The Lorenz attractor exists

    Författare :Warwick Tucker; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; MATEMATIK; MATHEMATICS; MATEMATIK; matematik; Mathematics;

    Sammanfattning : We prove that the Lorenz equations support a strange attractor, as conjectured by Edward Lorenz in 1963. We also prove that the attractor is robust, i.e., it persists under small perturbations of the coefficients in the underlying differential equations. LÄS MER

  3. 2. Computations of Automorphic Functions on Fuchsian Groups

    Författare :Helen Avelin; Andreas Strömbergsson; Dennis Hejhal; Warwick Tucker; Michael Rubinstein; Uppsala universitet; []
    Nyckelord :Mathematics; 11F72; 11F03; 11F06; 11Y35; 11-04; 11Y16; 33F06; 34B27; 33F05; MATEMATIK;

    Sammanfattning : This thesis consists of four papers which all deal with computations of automorphic functions on cofinite Fuchsian groups. In the first paper we develop an algorithm for numerical computation of the Eisenstein series. We focus in particular on the computation of the poles of the Eisenstein series. LÄS MER

  4. 3. Computational dynamics – real and complex

    Författare :Anna Belova; Warwick Tucker; Denis Gaidashev; Àlex Haro Provinciale; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Continued fractions; Generating functions; Rotation numbers; Rigorous computations; Interval analysis; Interval arithmetic; Multipliers; Quadratic map; Kuramoto-Sivashinsky equation; Mathematics; Matematik;

    Sammanfattning : The PhD thesis considers four topics in dynamical systems and is based on one paper and three manuscripts.In Paper I we apply methods of interval analysis in order to compute the rigorous enclosure of rotation number. LÄS MER

  5. 4. Computer-Assisted Proofs and Other Methods for Problems Regarding Nonlinear Differential Equations

    Författare :Oswald Fogelklou; Warwick Tucker; Gunilla Kreiss; Piotr Zgliczynski; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; computer-assisted proof; numerical verification; viscous Burgers’ equation; enclosure; existence; nonlinear boundary value problems; Euler equations; inverse problem; bicubic spline; interval analysis; heat equation; fluid limit; peer-to-peer networks; fixed points; stability; global stability; Mathematics; Matematik;

    Sammanfattning : This PhD thesis treats some problems concerning nonlinear differential equations. In the first two papers computer-assisted proofs are used. The differential equations there are rewritten as fixed point problems, and the existence of solutions are proved. LÄS MER

  7. 5. 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