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Rational Functions with a Polynomial Iterate

✍ Scribed by Joseph H. Silverman

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
161 KB
Volume
180
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let ⌽ z g ‫ރ‬ z be a rational function of degree d G 2. A well known theorem n Ε½ .

Ε½ . in dynamical systems says that if some iterate z s ( ( ΠΈΠΈΠΈ ( z is a 2 Ε½ . polynomial, then already z is a polynomial. More generally, this is true for Ε½ . Ε½ . Ε½ X Ε½ . . z g K z for any field K provided that is separable i.e., z / 0 . However, it need not be true for inseparable . In this note we give a complete description, in all characteristics and with no separability assumptions, of the rational functions which have a polynomial iterate.

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