Singularities of Differentiable Maps, Volume 1:Classification of Critical Points, Caustics and Wave Fronts

图书简介

?Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book?s sophisticated development permits readers to explore more applications than previous books on singularities.

Part I. Basic concepts.- The simplest examples.- The classes Sigma^ I .- The quadratic differential of a map.- The local algebra of a map and the Weierstrass preparation theorem.- The local multiplicity of a holomorphic map.- Stability and infinitesimal stability.- The proof of the stability theorem.- Versal deformations.- The classification of stable germs by genotype.- Review of further results.- Part II. Critical points of smooth functions.- A start to the classification of critical points.- Quasihomogeneous and semiquasihomogeneous singularities.- The classification of quasihomogeneous functions.- Spectral sequences for the reduction to normal forms.- Lists of singularities.- The determinator of singularities.- Real, symmetric and boundary singularities.- Part III. Singularities of caustics and wave fronts.- Lagrangian singularities.- Generating families.- Legendrian singularities.- The classification of Lagrangian and Legendrian singularities.- The bifurcation of caustics and wave fronts.- References.- Further references.- Subject Index.

Trade Policy 买家须知

关于产品：
● 正版保障：本网站隶属于中国国际图书贸易集团公司，确保所有图书都是100%正版。
● 环保纸张：进口图书大多使用的都是环保轻型张，颜色偏黄，重量比较轻。
● 毛边版：即书翻页的地方，故意做成了参差不齐的样子，一般为精装版，更具收藏价值。
关于退换货：
由于预订产品的特殊性，采购订单正式发订后，买方不得无故取消全部或部分产品的订购。
由于进口图书的特殊性，发生以下情况的，请直接拒收货物，由快递返回：
● 外包装破损/发错货/少发货/图书外观破损/图书配件不全（例如：光盘等）
并请在工作日通过电话400-008-1110联系我们。
签收后，如发生以下情况，请在签收后的5个工作日内联系客服办理退换货：
● 缺页/错页/错印/脱线
关于发货时间：
一般情况下：
●【现货】下单后48小时内由北京（库房）发出快递。
●【预订】【预售】下单后国外发货，到货时间预计5-8周左右，店铺默认中通快递，如需顺丰快递邮费到付。
● 需要开具发票的客户，发货时间可能在上述基础上再延后1-2个工作日（紧急发票需求，请联系010-68433105/3213）；
● 如遇其他特殊原因，对发货时间有影响的，我们会第一时间在网站公告，敬请留意。
关于到货时间：
由于进口图书入境入库后，都是委托第三方快递发货，所以我们只能保证在规定时间内发出，但无法为您保证确切的到货时间。
● 主要城市一般2-4天
● 偏远地区一般4-7天
关于接听咨询电话的时间：
010-68433105/3213正常接听咨询电话的时间为：周一至周五上午8：30～下午5：00，周六、日及法定节假日休息，将无法接听来电，敬请谅解。
其它时间您也可以通过邮件联系我们：customer@readgo.cn,工作日会优先处理。
关于快递：
● 已付款订单：主要由中通、宅急送负责派送，订单进度查询请拨打010-68433105/3213。

Singularities of Differentiable Maps, Volume 1:Classification of Critical Points, Caustics and Wave Fronts（Modern Birkh鋟ser Classics） 代数几何学

Singularities of Differentiable Maps, Volume 1:Classification of Critical Points, Caustics and Wave Fronts（Modern Birkh鋟ser Classics）
代数几何学