文档介绍：Contents Introduction CHAPTER I. An Analogue of the Bezout Theorem for a System of Real Elementary Equations 9 § L L General estimate of the number of roots of a system of equations 10 § . Estimate of the number of solutions of a system of quasipolynomials 12 §. A version of the general estimate of the number of roots of a system of equations 13 §. Estimate of the number of solutions of a system of trigonometric quasipolynomials 14 § . Elementary functions of many real variables t 6 §L6. Estimate of the number of solutions of a system of elementary equations 17 §. Remarks 18 CHAPTER II. Two Simple Versions of the Theory of FewnomiaiS 21 §. Rolle's theorem for dynamical systems 21 §. Algebraic propenies of P-curves 23 §. One more version of the theory of fewnomials 27 CHAPTER m. Analogues of the Theorems of Rolle and Bezout for Separating Solutions of Pfaff Equations 31 §. Coorientation and linking index 33 §. Separating submanifolds 36 Separating solutions of Pfaff equations 39 Separating solutions on l-dimensional manifolds; an analogue of Rolle's theorem 42 §. Higher-sional analogues of ROlle's estimate 45 §. Ordered systems of Pfaff equations, their separating solutions and characteristic ces 51 vii viii CONTENTS §. Estimate of the number of points in a zero-dimensional separating solution of an ordered system of Pfaff equations via the generalised number of zeroes of the characteristic sequence of the system 56 §. The virtual number of zeroes 62 §. Representative families of divlsorial sequences 65 §. The virtual number of zeroes on a manifold equipped with a volume form 68 §. Estimate of the irtual number of zeroeS of a sequence with isolated singular points via their order and index 73 §. A series of analogues of Rolle's estimate and Bezoufs theorem 76 §. Fewnomials in plex region and Newton polyhedra 81 §. Estimate of the number of ponents and the sum of the Betti numbers of higher-dimensional s