|
|
| |
| Small Cycles Property of Some Cremer RationalMaps and Polynomials |
| |
Citation： |
Rong FU,Ji ZHOU.Small Cycles Property of Some Cremer RationalMaps and Polynomials[J].Chinese Annals of Mathematics B,2024,45(1):123~136 |
| Page view： 348
Net amount： 289 |
Authors： |
Rong FU; Ji ZHOU |
|
|
| Abstract： |
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 C∞ of irrational numbers and show that if α ∈ C∞, then any rational map
is not linearizable and has infinitely many cycles in every neighborhood of the fixed point
with multiplier λ = e2πiα
. 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. |
Keywords： |
Irrationally indifferent fixed point, Linearization problem, Small cycles
property |
Classification： |
37F50 |
|
|
Download PDF Full-Text
|
|
|
|
