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:
“Helping children at a level of genuine intellectual inquiry takes imagination on the part of the adult. Even more, it takes the courage to become a resource in unfamiliar areas of knowledge and in ones for which one has no taste. But parents, no less than teachers, must respect a child’s mind and not exploit it for their own vanity or ambition, or to soothe their own anxiety.”
—Dorothy H. Cohen (20th century)
“If matrimony be really beneficial to society, the custom that ... married women alone are allowed any claim to place, is as useful a piece of policy as ever was invented.... The ridicule fixed on the appellation of old maid hath, I doubt not, frightened a very large number into the bonds of wedlock.”
—Sarah Fielding (1710–1768)
“The weakness of the man who, when his theory works out into a flagrant contradiction of the facts, concludes “So much the worse for the facts: let them be altered,” instead of “So much the worse for my theory.””
—George Bernard Shaw (1856–1950)
“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)