Horizontal systems of rays arise in the study of integral curves of Hamiltonian systems on T*X, which are tangent to a given distribution V of hyperplanes on X. We investigate the local properties of systems of rays for general pairs (H,V) as well as for Hamiltonians H such that the corresponding Hamiltonian vector fields are horizontal with respect to V. As an example we explicitly calculate the space of horizontal geodesics and the corresponding systems of rays for the canonical distribution on the Heisenberg group. Local stability of systems of horizontal rays based on the standard singularity theory of Lagrangian submanifolds is also considered.
@article{bwmeta1.element.bwnjournal-article-bcpv32z1p245bwm,
author = {Janeczko, S.},
title = {Systems of rays in the presence of distribution of hyperplanes},
journal = {Banach Center Publications},
volume = {31},
year = {1995},
pages = {245-260},
zbl = {0844.57030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p245bwm}
}
Janeczko, S. Systems of rays in the presence of distribution of hyperplanes. Banach Center Publications, Tome 31 (1995) pp. 245-260. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p245bwm/
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