Integer sequences counting periodic points
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Publication:6471796
arXivmath/0204173MaRDI QIDQ6471796
Graham Everest, Yash Puri, Alfred J. van der Poorten, Thomas B. Ward
Publication date: 13 April 2002
Abstract: An existing dialogue between number theory and dynamical systems is advanced. A combinatorial device gives necessary and sufficient conditions for a sequence of non-negative integers to count the periodic points in a dynamical system. This is applied to study linear recurrence sequences which count periodic points. Instances where the -parts of an integer sequence themselves count periodic points are studied. The Mersenne sequence provides one example, and the denominators of the Bernoulli numbers provide another. The methods give a dynamical interpretation of many classical congruences such as Euler-Fermat for matrices, and suggest the same for the classical Kummer congruences satisfied by the Bernoulli numbers.
Bernoulli and Euler numbers and polynomials (11B68) Recurrences (11B37) Topological entropy (37B40) Arithmetic properties of periodic points (37P35)
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