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Homotopy Invariants of Time Reversible Periodic Orbits I. Theory

โœ Scribed by Bernold Fiedler; Steffen Heinze

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
601 KB
Volume
126
Category
Article
ISSN
0022-0396

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โœฆ Synopsis

We introduce a family of homotopy invariants deg n (#), n=1, 2, 3, . . . associated to a reversible periodic orbit # of a time reversible system. We present two results:

(i) we compute deg n (#) from information on the Floquet multipliers of #, (ii) conversely, we recover any Floquet multipliers of # on the unit circle from the sequence deg n (#).

1996 Academic Press, Inc.

(i) the Kolmogorov Petrovski Piskunov (KPP) equation, g =u(1&u);

(ii) the Chafee-Infante problem, g=u(1&u 2 );

(iii) the pendulum equation, g=sin u;

(iv) the Euler rod, g=u -1&u* 2 ;

article no.

๐Ÿ“œ SIMILAR VOLUMES

Homotopy Invariants of Time Reversible P
Homotopy Invariants of Time Reversible Periodic Orbits II. Towards Applications
โœ Bernold Fiedler; Steffen Heinze ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 599 KB

For a reversible periodic orbit # we apply the sequence of homotopy invariants deg n (#), n=1, 2, 3, ..., defined in [Fiedler 6 Heinze] (1996), We use this sequence to prove a global bifurcation result for reversible periodic orbits with prescribed minimal period. This result will be applied to seco