Abstract
This paper deals with the brake orbits of Hamiltonian system 
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
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Partially supported by NNSF of China (10571085) and Science Foundation of Hohai University.
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An, T. The Brake Orbits of Hamiltonian Systems on Positive-type Hypersurfaces. Positivity 10, 681–692 (2006). https://doi.org/10.1007/s11117-006-0051-4
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DOI: https://doi.org/10.1007/s11117-006-0051-4