LEADER 02897nam a2200433 i 4500
001 991003635909707536
006 m     o  d        
007 cr cnu|||unuuu
008 190405s2018    sz a    ob    001 0 eng d
020   $a9783319788104$q(electronic bk.)
020   $a3319788108$q(electronic bk.)
020   $z9783319788098$q(print)
020   $z3319788094
024 7 $a10.1007/978-3-319-78810-4$2doi
035   $ab14363847-39ule_inst
040   $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng
082 04$a511.322$223
084   $aAMS 37-02
100 1 $aZakeri, Saeed$0756217
245 10$aRotation sets and complex dynamics$h[e-book] /$cSaeed Zakeri
264  1$aCham, Switzerland :$bSpringer,$c2018
300   $a1 online resource (xiv, 124 pages) :$billustrations (some color)
336   $atext$btxt$2rdacontent
337   $acomputer$bc$2rdamedia
338   $aonline resource$bcr$2rdacarrier
347   $atext file$bPDF$2rda
490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2214
504   $aIncludes bibliographical references and index
505 0 $a1. Monotone Maps of the Circle ; 2. Rotation Sets ; 3. The Deployment Theorem ; 4. Applications and Computations ; 5. Relation to Complex Dynamics
520   $aThis monograph examines rotation sets under the multiplication by d (mod 1) map and their relation to degree d polynomial maps of the complex plane. These sets are higher-degree analogs of the corresponding sets under the angle-doubling map of the circle, which played a key role in Douady and Hubbard's work on the quadratic family and the Mandelbrot set. Presenting the first systematic study of rotation sets, treating both rational and irrational cases in a unified fashion, the text includes several new results on their structure, their gap dynamics, maximal and minimal sets, rigidity, and continuous dependence on parameters. This abstract material is supplemented by concrete examples which explain how rotation sets arise in the dynamical plane of complex polynomial maps and how suitable parameter spaces of such polynomials provide a complete catalog of all such sets of a given degree. As a main illustration, the link between rotation sets of degree 3 and one-dimensional families of cubic polynomials with a persistent indifferent fixed point is outlined. The monograph will benefit graduate students as well as researchers in the area of holomorphic dynamics and related fields
650  0$aSet theory
650  0$aRotational motion
650  0$aErgodic theory
856 40$zAn electronic book accessible through the World Wide Web$uhttp://link.springer.com/10.1007/978-3-319-78810-4
907   $a.b14363847$b03-03-22$c05-04-19
912   $a991003635909707536
996   $aRotation sets and complex dynamics$91524085
997   $aUNISALENTO
998   $ale013$b05-04-19$cm$d@  $e-$feng$gsz $h0$i0