Authors: F. PUGLIESE, A. M. VINOGRADOV
It is shown that a lagrangian system whose Legendre transformation
degenerates along a hypersurface behaves in a strange manner by jumping from
time to time without any ''visible cause''. In such a jump the system
changes instantaneously its coordinates as well as its momenta. The
mathematical dscription of the phenomenon is based on the theory of impact,
refraction and reflection developed by one of the authors and the
observation that a hamiltonian vector field, understood as a relative one,
can be associated with any lagrangian, degenerated or not. Necessary
elements of the general theory of such systems are reported and a detailed
description of a post-relativistic oscillator showing such a behaviour is
28 pages, LaTeX-2e (AmSLaTeX 1.2+Epsf), 11 figures (EPS-format).
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