LEADER 03223nam 22005415 450 001 9910300125003321 005 20200704104945.0 010 $a3-319-78810-8 024 7 $a10.1007/978-3-319-78810-4 035 $a(CKB)3810000000358723 035 $a(DE-He213)978-3-319-78810-4 035 $a(MiAaPQ)EBC6296106 035 $a(PPN)229494080 035 $a(EXLCZ)993810000000358723 100 $a20180623d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRotation Sets and Complex Dynamics /$fby Saeed Zakeri 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XIV, 124 p. 34 illus., 32 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2214 311 $a3-319-78809-4 327 $a1. Monotone Maps of the Circle -- 2. Rotation Sets -- 3. The Deployment Theorem -- 4. Applications and Computations -- 5. Relation to Complex Dynamics. 330 $aThis monograph examines rotation sets under the multiplication by d (mod 1) map and their relation to degree d polynomial maps of the complex plane. These sets are higher-degree analogs of the corresponding sets under the angle-doubling map of the circle, which played a key role in Douady and Hubbard's work on the quadratic family and the Mandelbrot set. Presenting the first systematic study of rotation sets, treating both rational and irrational cases in a unified fashion, the text includes several new results on their structure, their gap dynamics, maximal and minimal sets, rigidity, and continuous dependence on parameters. This abstract material is supplemented by concrete examples which explain how rotation sets arise in the dynamical plane of complex polynomial maps and how suitable parameter spaces of such polynomials provide a complete catalog of all such sets of a given degree. As a main illustration, the link between rotation sets of degree 3 and one-dimensional families of cubic polynomials with a persistent indifferent fixed point is outlined. The monograph will benefit graduate students as well as researchers in the area of holomorphic dynamics and related fields. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2214 606 $aDynamics 606 $aErgodic theory 606 $aFunctions of complex variables 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aFunctions of complex variables. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aFunctions of a Complex Variable. 676 $a511.322 700 $aZakeri$b Saeed$4aut$4http://id.loc.gov/vocabulary/relators/aut$0756217 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300125003321 996 $aRotation sets and complex dynamics$91524085 997 $aUNINA