Cubic Polynomials with Periodic Cycles of a Specified Multiplier
Canadian journal of mathematics, Tome 64 (2012) no. 2, pp. 318-344
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We consider cubic polynomials $f\left( z \right)\,=\,{{z}^{3}}\,+\,az\,+\,b$ defined over $\mathbb{C}\left( \lambda\right)$ , with a marked point of period $N$ and multiplier $\lambda$ . In the case $N\,=\,1$ , there are infinitely many such objects, and in the case $N\,\ge \,3$ , only finitely many (subject to a mild assumption). The case $N\,=\,2$ has particularly rich structure, and we are able to describe all such cubic polynomials defined over the field ${{\cup }_{n\ge 1}}\,\mathbb{C}\left( {{\lambda }^{1/n}} \right)$ .
Mots-clés :
37P35, cubic polynomials, periodic points, holomorphic dynamics
Ingram, Patrick. Cubic Polynomials with Periodic Cycles of a Specified Multiplier. Canadian journal of mathematics, Tome 64 (2012) no. 2, pp. 318-344. doi: 10.4153/CJM-2011-093-8
@article{10_4153_CJM_2011_093_8,
author = {Ingram, Patrick},
title = {Cubic {Polynomials} with {Periodic} {Cycles} of a {Specified} {Multiplier}},
journal = {Canadian journal of mathematics},
pages = {318--344},
year = {2012},
volume = {64},
number = {2},
doi = {10.4153/CJM-2011-093-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-093-8/}
}
TY - JOUR AU - Ingram, Patrick TI - Cubic Polynomials with Periodic Cycles of a Specified Multiplier JO - Canadian journal of mathematics PY - 2012 SP - 318 EP - 344 VL - 64 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-093-8/ DO - 10.4153/CJM-2011-093-8 ID - 10_4153_CJM_2011_093_8 ER -
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