Open AccessOn the Number of Rational Iterated Pre-Images of -1 under Quadratic Dynamical Systems
Author(s) -
Trevor Hyde
Publication year - 2010
Publication title -
american journal of undergraduate research
Language(s) - English
Resource type - Journals
eISSN - 2375-8732
pISSN - 1536-4585
DOI - 10.33697/ajur.2010.010
Subject(s) - rational number , iterated function , quadratic equation , mathematics , class (philosophy) , rational function , upper and lower bounds , discrete mathematics , combinatorics , pure mathematics , computer science , mathematical analysis , geometry , artificial intelligence
For the class of functions fc x = x 2 + c, we prove a conditional bound on the number of rational solutions to fc N x = −1 and make computational conjectures for a bound on the number of rational solutions to fc N x = a for a in a specific subset of the rationals.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom