Other Areas in Which Number Theory and Dynamics Interact
There are many other problems of a number theoretic nature that appear in the setting of dynamical systems, including:
- dynamics over finite fields.
- dynamics over function fields such as C(x).
- iteration of formal and p-adic power series.
- dynamics on Lie groups.
- arithmetic properties of dynamically defined moduli spaces.
- equidistribution and invariant measures, especially on p-adic spaces.
- dynamics on Drinfeld modules.
- number-theoretic iteration problems that are not described by rational maps on varieties, for example, the Collatz problem.
The Arithmetic Dynamics Reference List gives an extensive list of articles and books covering a wide range of arithmetical dynamical topics.
Read more about this topic: Arithmetic Dynamics
Famous quotes containing the words areas, number, theory, dynamics and/or interact:
“The point is, that the function of the novel seems to be changing; it has become an outpost of journalism; we read novels for information about areas of life we don’t know—Nigeria, South Africa, the American army, a coal-mining village, coteries in Chelsea, etc. We read to find out what is going on. One novel in five hundred or a thousand has the quality a novel should have to make it a novel—the quality of philosophy.”
—Doris Lessing (b. 1919)
“I am walking over hot coals suspended over a deep pit at the bottom of which are a large number of vipers baring their fangs.”
—John Major (b. 1943)
“... liberal intellectuals ... tend to have a classical theory of politics, in which the state has a monopoly of power; hoping that those in positions of authority may prove to be enlightened men, wielding power justly, they are natural, if cautious, allies of the “establishment.””
—Susan Sontag (b. 1933)
“Anytime we react to behavior in our children that we dislike in ourselves, we need to proceed with extreme caution. The dynamics of everyday family life also have a way of repeating themselves.”
—Cathy Rindner Tempelsman (20th century)
“Art and ideology often interact on each other; but the plain fact is that both spring from a common source. Both draw on human experience to explain mankind to itself; both attempt, in very different ways, to assemble coherence from seemingly unrelated phenomena; both stand guard for us against chaos.”
—Kenneth Tynan (1927–1980)