## Geometry and Topology of Caustics: Caustics '98Stanisław Janeczko, V. M. Zakalyukin |

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### Contents

BANACH CENTER PUBLICATIONS VOLUME 50 | 11 |

CONTENTS | 19 |

N BENSALEM and F PELLETIER Some geometrical properties of inﬁnite | 41 |

Copyright | |

17 other sections not shown

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### Common terms and phrases

afﬁne boundary break point cactus caustic closed curve codimension coefﬁcients condition conﬂict set consider convex hull coordinates cooriented corresponding cotangent bundle critical points critical value curvature curve segment deﬁned deﬁnition denote diagrams diffeomorphism differential dimension English transl Figure ﬁnd ﬁnite ﬁrst ﬂattening points genotype geodesic geometric germ given Grassmannian Hilbert hypersurface inﬁexion inﬁnitesimal inﬂection integrable intersection invariants Lagrange stable Lagrangian Lagrangian submanifold Legendrian knots Lemma Lie algebra Lie group linear manifold map-germ f mapping Maslov Math minimal loop Monge-Ampere equations multiplicity nilpotent normal form open Whitney umbrella orbits orientation osculating hyperplane pair pair-mapping passport plane curve polynomial projection Proof PROPOSITION quasihomogeneous resp rhamphoid cusp right-left equivalence satisﬁed Section self-tangencies singularities singularity theory smooth solutions strata stratum structure submanifold subspaces surface symmetry symplectic Theorem topological transversal umbilic points umbilics V. I. Arnol'd vector ﬁeld versal wave front Whitney umbrella