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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
  • Polynomial
  • Iterate
  • Fixed Point
  • Periodic Point And Cycle
  • Repelling Periodic Point And Cycle
  • Nonrepelling Periodic Point And Cycle

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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