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On invariant closed curves for one-step methods (1987)

Beyn, Wolf-Jürgen

Springer

Numerische Mathematik 51 (1987), S. 103-122

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ISSN: 0945-3245

Schlagwort(e): AMS(MOS) 65L05, 58F08, 58F22 ; CR: G1.7

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Summary We show that a one-step method as applied to a dynamical system with a hyperbolic periodic orbit, exhibits an invariant closed curve for sufficiently small step size. This invariant curve converges to the periodic orbit with the order of the method and it inherits the stability of the periodic orbit. The dynamics of the one-step method on the invariant curve can be described by the rotation number for which we derive an asymptotic expression. Our results complement those of [2, 3] where one-step methods were shown to create invariant curves if the dynamical system has a periodic orbit which is stable in either time direction or if the system undergoes a Hopf bifurcation.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01399697

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Digitale Medien

Ellipsometric investigation of single crystalline Cz—Si subjected to hydrostatic pressure (1994)

Kamińska, Anna M. ; Misiuk, Andrzej ; Wolf, Jürgen

Chichester [u.a.] : Wiley-Blackwell

Surface and Interface Analysis 22 (1994), S. 346-349

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ISSN: 0142-2421

Schlagwort(e): Chemistry ; Polymer and Materials Science

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Physik

Notizen: The application of ellipsometry to study the SiOx/Si system subjected to hydrostatic pressures up to 1.8 GPa at temperatures up to 1280 °C is described. The theoretical model of defects as the spherical disturbances of material has been assumed. The ellipsometric parameters have been analysed as a function of defects size and density and compared with data obtained by etching and x-ray methods. The applicability of ellipsometry for near-surface defect structure analysis has been discussed.

Zusätzliches Material: 4 Ill.