LEADER 02770nam 2200433 450 001 9910149709403321 005 20230810000039.0 010 $a981-4635-37-5 035 $a(CKB)2660000000040934 035 $a(MiAaPQ)EBC4731829 035 $a(WSP)00009395 035 $a(EXLCZ)992660000000040934 100 $a20160823h20172017 uy| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aDynamical scale transform in tropical geometry /$fTsuyoshi Kato (Kyoto University, Japan) 210 1$aNew Jersey :$cWorld Scientific,$d[2017] 210 4$dİ2017 215 $a1 online resource (270 pages) 300 $aTitle from PDF file title page (viewed November 11, 2016). 311 $a981-4635-36-7 320 $aIncludes bibliographical references and index. 330 $a"This book provides comprehensive analysis of dynamical systems in tropical geometry, which include the author's significant discoveries and pioneering contributions. Tropical geometry is a kind of dynamical scale transform which connects real rational dynamics with piecewise linear one presented by max and plus algebras. A comparison method is given which estimates orbits corresponding to different rational dynamics by reduction to the piecewise linear dynamics. Both rational and piecewise linear dynamics appear in many important branches of mathematics. Tropical geometry can play a role or function to bridge between different subjects in mathematics. This book contains detailed accounts of basic strategy on how to apply tropical geometry to analysis in various mathematical subjects by presenting several applications which include: a rough classification of partial differential equations from the point of view of global behavior of solutions; construction of the infinite quasi-recursive rational dynamics, based on the automaton of the Burnside group by Aleshin-Grigorchuk; study on nearly periodicity of the pentagram map on the moduli space of the twisted polygons; spectral coincidence between lamplighter group in theory of automata groups and Box and ball systems corresponding to KdV equation in soliton theory. This book is self-contained, and detailed accounts of theory of automata groups, BBS and the pentagram map are also included."--Publisher's website. 606 $aTropical geometry 606 $aGeometry, Algebraic 615 0$aTropical geometry. 615 0$aGeometry, Algebraic. 676 $a516.3/5 700 $aKato$b Tsuyoshi$f1961-$01249816 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910149709403321 996 $aDynamical scale transform in tropical geometry$92896108 997 $aUNINA