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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 375-376 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A variation of the lemma of Jacobson–Morozov on the imbedding of a nonzero nilpotent element of the real symplectic algebra into the split simple three-dimensional Lie algebra is proved. The proof is algorithmic and relies on our earlier work on the theory of normal forms for the real symplectic algebra.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 46 (1995), S. 85-106 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A new notion of shadowing of a pseudo orbit, an approximate solution, of an autonomous system of ordinary differential equations by an associated nearby true orbit is introduced. Then a general theorem which guarantees the existence of shadowing of pseudo orbits in compact hyperbolic sets is proved.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Monatshefte für Mathematik 98 (1984), S. 53-63 
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Momentum mapping of an autonomous, real linear Hamiltonian system is determined by its set of quadratic integrals. Such a system can be identified with an element of the real symplectic algebra and its quadratic integrals correspond to the centralizer of this element inside the symplectic algebra. In this paper, using a new set of normal forms for the elements of the real symplectic algebra, we compute their centralizers explicitly.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Numerical algorithms 14 (1997), S. 55-78 
    ISSN: 1572-9265
    Keywords: Primary 34C25, 65L70 ; Secondary 65L07
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A general theorem for establishing the existence of a true periodic orbit near a numerically computed pseudoperiodic orbit of an autonomous system of ordinary differential equations is presented. For practical applications, a Newton method is devised to compute appropriate pseudoperiodic orbits. Then numerical considerations for checking the hypotheses of the theorem in terms of quantities which can be computed directly from the pseudoperiodic orbit and the vector field are addressed. Finally, a numerical method for estimating the Lyapunov exponents of the true periodic orbit is given. The theory and computations are designed to be applicable for unstable periodic orbits with long periods. The existence of several such periodic orbits of the Lorenz equations is exhibited.
    Type of Medium: Electronic Resource
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  • 5
    Book
    Book
    New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest :Springer,
    Title: Dynamics and bifurcations /; 3
    Author: Hale, Jack K.
    Contributer: Koçak, Hüseyin
    Publisher: New York ; Berlin ; Heidelberg ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest :Springer,
    Year of publication: 1991
    Pages: XIV, 568 S. : , Ill., graph. Darst. ; , 25 cm
    Series Statement: Texts in applied mathematics 3
    ISBN: 3-540-97141-6 , 0-387-97141-6
    Type of Medium: Book
    Language: German
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