Small Cycles Property of Some Cremer Rational Maps and Polynomials  

Small Cycles Property of Some Cremer Rational Maps and

作　　者：Rong FU Ji ZHOU 

机构地区：[1]Faculty of Science,Yibin University,Yibin 644000,Sichuan,China [2]Department of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,China

出　　处：《Chinese Annals of Mathematics,Series B》2024年第1期123-136,共14页数学年刊（B辑英文版）

摘　　要：This paper concerns the linearization problem on rational maps of degree d≥2 and polynomials of degree d>2 from the perspective of non-linearizability.The authors introduce a set l_(∞) of irrational numbers and show that if α∈l_(∞),then any rational map is not linearizable and has infinitely many cycles in every neighborhood of the fixed point with multiplier λ=e^(2πiα),Adding more constraints to cubic polynomials,they discuss the above problems by polynomial-like maps.For the family of polynomials,with the help of Yoccoz's method,they obtain its maximum dimension of the set in which the polynomials are non-linearizable.

关 键 词：Irrationally indifferent fixed point Linearization problem Small cycles property 

分 类 号：O19[理学—数学]