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Misiurewicz polynomials and dynamical units, part II.
- Source :
-
Research in Number Theory . 6/11/2024, Vol. 10 Issue 3, p1-24. 24p. - Publication Year :
- 2024
-
Abstract
- Fix an integer d ≥ 2 . The parameters c 0 ∈ Q ¯ for which the unicritical polynomial f d , c (z) = z d + c ∈ C [ z ] has finite postcritical orbit, also known as Misiurewicz parameters, play a significant role in complex dynamics. Recent work of Buff, Epstein, and Koch proved the first known cases of a long-standing dynamical conjecture of Milnor using their arithmetic properties, about which relatively little is otherwise known. Continuing our work from a companion paper, we address further arithmetic properties of Misiurewicz parameters, especially the nature of the algebraic integers obtained by evaluating the polynomial defining one such parameter at a different Misiurewicz parameter. In the most challenging such combinations, we describe a connection between such algebraic integers and the multipliers of associated periodic points. As part of our considerations, we also introduce a new class of polynomials we call p-special, which may be of independent number theoretic interest. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POLYNOMIALS
*ORBITS (Astronomy)
*ARITHMETIC
*INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 25220160
- Volume :
- 10
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Research in Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 177816825
- Full Text :
- https://doi.org/10.1007/s40993-024-00539-0