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 ψ∞ of irrational numbers and show that if a ∈ ψ∞,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.
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