Browsing by Subject "quadratic map"

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    Arithmetic properties of 3-cycles of quadratic maps over Q
    (Elsevier, 2022-11) Morton, Patrick; Raianu, Serban; Mathematical Sciences, School of Science
    It is shown that c = -29/16 is the unique rational number of smallest denominator, and the unique rational number of smallest numerator, for which the map fc(x) = x2 + c has a rational periodic point of period 3. Several arithmetic conditions on the set of all such rational numbers c and the rational orbits of fc(x) are proved. A graph on the numerators of the rational 3-periodic points of maps fc is considered which reflects connections between solutions of norm equations from the cubic field of discriminant -23.