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03147aam a2200373 i 4500 001 7752DD3AE23911EC9D80461122ECA4DB 003 SILO 005 20220602010055 008 210710t20212021enka b 001 0 eng 010 $a 2021024708 020 $a 131660621X 020 $a 9781316606216 020 $a 1107151643 020 $a 9781107151642 035 $a (OCoLC)1237252054 040 $a LBSOR/DLC $b eng $e rda $c DLC $d UKMGB $d OCLCF $d YDX $d OCLCO $d YDX $d OCL $d QGE $d UIU $d SILO 042 $a pcc 050 00 $a QA614.58 M66 2021 084 $a MAT038000 $2 bisacsh 100 1 $a Montaldi, J. $q (James), $e author. 245 10 $a Singularities, bifurcations and catastrophes / $c James Montaldi. 264 1 $a Cambridge, United Kingdom ; $b Cambridge University Press, $c 2021. 300 $a xvii, 430 pages : $b illustrations (some color) ; $c 26 cm 504 $a Includes bibliographical references and index. 505 0 $a What's it all about? -- Families of functions -- The ring of germs of smooth functions -- Right equivalence -- Finite determinacy -- Classification of the elementary catastrophes -- Unfoldings & catastrophes -- Singularities of plane curves -- Even functions -- Families of maps and bifurcations -- Contact equivalence -- Tangent spaces -- Classification for contact equivalence -- Contact equivalence and unfoldings -- Geometric applications -- Preparation theorem -- Left-right equivalence -- Bifurcation problems and paths -- Vector fields tangent to a variety -- Kv-equivalence -- Classification of paths -- Loose ends -- Constrained bifurcation problems. 520 $a "Suitable for advanced undergraduates, postgraduates and researchers, this self-contained textbook provides an introduction to the mathematics lying at the foundations of bifurcation theory. The theory is built up gradually, beginning with the well-developed approach to singularity theory through right-equivalence. The text proceeds with contact equivalence of map-germs and finally presents the path formulation of bifurcation theory. This formulation, developed partly by the author, is more general and more flexible than the original one dating from the 1980s. A series of appendices discuss standard background material, such as calculus of several variables, existence and uniqueness theorems for ODEs, and some basic material on rings and modules. Based on the author's own teaching experience, the book contains numerous examples and illustrations. The wealth of end-of-chapter problems develop and reinforce understanding of the key ideas and techniques: solutions to a selection are provided"-- $c Provided by publisher. 650 0 $a Singularities (Mathematics) $v Textbooks. 650 0 $a Bifurcation theory $v Textbooks. 650 0 $a Catastrophes (Mathematics) $v Textbooks. 776 08 $i Online version: $a Montaldi, James. $t Singularities, bifurcations and catastrophes $d Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2021 $z 9781107151642 $w (DLC) 2021024709 941 $a 1 952 $l USUX851 $d 20220802021047.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=7752DD3AE23911EC9D80461122ECA4DB 994 $a C0 $b IWAInitiate Another SILO Locator Search