caa a22 4500 60623330X CHVBK 20210128101231.0 cr unu---uuuuu 210128e20150701xx s 000 0 eng 10.1007/s10883-014-9240-9 doi (NATIONALLICENCE)springer-10.1007/s10883-014-9240-9 Kourliouros Konstantinos Imperial College London, London, UK aut Singularities of Functions on the Martinet Plane, Constrained Hamiltonian Systems and Singular Lagrangians [Elektronische Daten] [Konstantinos Kourliouros] We consider here the analytic classification of pairs (ω, f) where ω is a germ of a 2-form on the plane and f is a function germ with isolated singularities. We consider the case where ω is singular, i.e., it vanishes nondegenerately along a smooth line H(ω) (Martinet case) and the function f is such that the pair (f, H(ω)) defines a simple boundary singularity. In analogy with the ordinary case (for symplectic forms on the plane), we show that the moduli in the classification problem are analytic functions of 1-variable and that their number is exactly equal to the Milnor number of the corresponding boundary singularity. Moreover, we derive a normal form for the pair (ω, f) involving exactly these functional invariants. Finally, we give an application of the results in the theory of constrained Hamiltonian systems, related to the motion of charged particles in the quantization limit in an electromagnetic field, which in turn leads to a list of normal forms of generic singular Lagrangians (of first order in the velocities) on the plane. Springer Science+Business Media New York, 2014 Singular symplectic structures nationallicence Boundary singularities nationallicence Normal forms nationallicence Constrained Hamiltonian systems nationallicence Singular Lagrangians nationallicence Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/3(2015-07-01), 401-422 1079-2724 21:3<401 2015 21 10883 https://doi.org/10.1007/s10883-014-9240-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10883-014-9240-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kourliouros Konstantinos Imperial College London, London, UK aut NATIONALLICENCE 773 0- Journal of Dynamical and Control Systems Springer US; http://www.springer-ny.com 21/3(2015-07-01), 401-422 1079-2724 21:3<401 2015 21 10883