A class of Hamiltonian deformations of plane curves is defined and studied. Hamiltonian deformations of conics and cubics are considered as illustrative examples. These deformations are described by systems of hydrodynamical-type equations. It is shown that solutions of these systems describe processes of formation of singularities (cusps, nodes), bubbles and change of the genus of a curve. © 2010 IOP Publishing Ltd.
Hamiltonian motions of plane curves and formation of singularities and bubbles
ORTENZI, GIOVANNI
2010-01-01
Abstract
A class of Hamiltonian deformations of plane curves is defined and studied. Hamiltonian deformations of conics and cubics are considered as illustrative examples. These deformations are described by systems of hydrodynamical-type equations. It is shown that solutions of these systems describe processes of formation of singularities (cusps, nodes), bubbles and change of the genus of a curve. © 2010 IOP Publishing Ltd.
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