# Polynomials without repelling periodic point of given period

- Authors
- Journal
- Journal of Mathematical Analysis and Applications 0022-247X
- Publisher
- Elsevier
- Publication Date
- Volume
- 324
- Issue
- 1
- Identifiers
- DOI: 10.1016/j.jmaa.2005.11.075
- Keywords

## Abstract

Abstract Bergweiler proved that for any given integer k ⩾ 2 , every polynomial P of degree d ⩾ 2 has at least one repelling periodic cycle of period k unless ( k , d ) ∈ { ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 2 ) } . Here we classified these exceptional polynomials. We also showed that the Julia sets of these exceptional polynomials are connected.

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