14247

12893

كارشناسي ارشد

رياضي كاربردي

اصفهان : دانشگاه صنعتي اصفهان

1397

پانزده، ۱۸۰ص.: مصور

انگليسي به فارسي; فارسي به انگليسي

1397/10/26

كتابنامه

رياضي

رياضي

ID12893

Tongues in degree 4 Blaschke products Safora Rezaei Adaryani safora rezaei@math iut ac ir December 19 2018 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamid Reza Zohouri Zangeneh hamidz@cc iut ac ir Advisor Dr Rasoul Asheghi r asheghi@cc iut ac ir 2010 MSC 37F45 37F10 37F50 37E10 Keywords holomorphic dynamics Blaschke products circle maps tongues AbstractGiven a rational map f C C where C C denotes the Riemann sphere we considerthe dynamical system given by the iterates of f The Riemann sphere splits into two totally f invariant subsets the Fatou set F f which is defined to be the set of points z C where the family f n n N is normal in some neighborhood of z and its complement the Julia set J f Thedynamics of the points in F f are stable in the sense of normality or equicontinuity whereas thedynamics in J f present chaotic behavior The Fatou set is open and its connected components called Fatou components are mapped under f among themselves All Fatou components of a rationalmap are either periodic or preperiodic see 90 By means of the Classification Theorem c f 67 any periodic Fatou component of a rational map is either the basin of attraction of an attracting orparabolic cycle or a simply connected rotation domain a Siegel disk or a doubly connected rotationdomain a Herman ring Moreover any such component is somehow related to a critical point i e a point z C such that f z 0 Indeed the basin of attraction of an attracting or parabolic cyclecontains at least a critical point whereas Siegel disks and Herman rings have critical orbits orbits

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رسول عاشقي

محمود منجگاني، رسول كاظمي