Cyclic Structure of Dynamical Systems
نویسندگان
چکیده
In the case d = 1, the properties of the system D = D1 are the subject of the well-known 3x + 1 conjecture. For every one of 6667 systems Dd, 1 ≤ d ≤ 19999, we calculate its (complete, as we argue) list of primitive cycles. We unite in a single conceptual framework of primitive memberships, and we experimentally confirm three primitive cycles conjectures of Jeff Lagarias. An in-deep analysis of the diophantine formulae for primitive cycles, together with new rich experimental data, suggest several new conjectures, theoretically studied and experimentally confirmed in the present paper. As a part of this program, we prove a new upper bound to the number of primitive cycles of a given oddlength.
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