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Local Controllability around Closed Orbits

100%
Grochowski M.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2014
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tom 62
|
nr 1
77-85
EN
We give a necessary and sufficient condition for local controllability around closed orbits for general smooth control systems. We also prove that any such system on a compact manifold has a closed orbit.
2
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Reachable sets for a class of contact sub-lorentzian metrics on ℝ³, and null non-smooth geodesics

100%
Grochowski M.
Banach Center Publications
|
2008
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tom 82
|
nr 1
101-110
EN
We compute future timelike and nonspacelike reachable sets from the origin for a class of contact sub-Lorentzian metrics on ℝ³. Then we construct non-smooth (and therefore non-Hamiltonian) null geodesics for these metrics. As a consequence we deduce that the sub-Lorentzian distance from the origin is continuous at points belonging to the boundary of the reachable set.
3
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On the Heisenberg sub-Lorentzian metric on ℝ³

100%
Grochowski M.
Banach Center Publications
|
2004
|
tom 65
|
nr 1
57-65
EN
In this paper we study properties of the Heisenberg sub-Lorentzian metric on ℝ³. We compute the conjugate locus of the origin, and prove that the sub-Lorentzian distance in this case is differentiable on some open set. We also prove the existence of regular non-Hamiltonian geodesics, a phenomenon which does not occur in the sub-Riemannian case.
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