The Brake Orbits of Hamiltonian Systems on Positive-type Hypersurfaces

The Brake Orbits of Hamiltonian Systems on Positive-type Hypersurfaces This paper deals with the brake orbits of Hamiltonian system [InlineMediaObject not available: see fulltext.] on given energy hypersurfaces Σ = H −1(1). We introduce a class of contact type but not necessarily star-shaped hypersurfaces in ℝ2n and call them normalized positive-type hypersurfaces. By using of the critical point theory, we prove that if Σ is a partially symmetric normalized positive-type hypersurface, it must carries a brake orbit of (HS). Furthermore, we obtain some multiplicity results under certain pinching conditions. Our results include the earlier works on this subject given by P. Rabinowitz and A. Szulkin in star-shaped case. An example of partially symmetric normalized positive-type hypersurface in ℝ4 that is not star-shaped is also presented http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

The Brake Orbits of Hamiltonian Systems on Positive-type Hypersurfaces

Positivity , Volume 10 (4) – Jul 11, 2006
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Publisher
Birkhäuser-Verlag
Copyright
Copyright © 2006 by Birkhäuser Verlag, Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-006-0051-4
Publisher site
See Article on Publisher Site

Abstract

This paper deals with the brake orbits of Hamiltonian system [InlineMediaObject not available: see fulltext.] on given energy hypersurfaces Σ = H −1(1). We introduce a class of contact type but not necessarily star-shaped hypersurfaces in ℝ2n and call them normalized positive-type hypersurfaces. By using of the critical point theory, we prove that if Σ is a partially symmetric normalized positive-type hypersurface, it must carries a brake orbit of (HS). Furthermore, we obtain some multiplicity results under certain pinching conditions. Our results include the earlier works on this subject given by P. Rabinowitz and A. Szulkin in star-shaped case. An example of partially symmetric normalized positive-type hypersurface in ℝ4 that is not star-shaped is also presented

Journal

PositivitySpringer Journals

Published: Jul 11, 2006

References

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