KNASTER AND FRIENDS III: SUBADDITIVE COLORINGS

Kingman's Subadditive Ergodic Theorem Kingman's Subadditive Ergodic Theorem

A simple proof of Kingman’s subadditive ergodic theorem is developed from a point of view which is conceptually algorithmic and which does not rely on either a maximal inequality or a combinatorial Riesz lemma.

Open Maps between Knaster Continua

We i n vestigate the set of open maps from one Knaster continuum to another. A structure theorem for the semigroup of open induced maps on a Knaster continuum is obtained. Homeomorphisms w h i c h are not induced are constructed, and it is shown that the induced open maps are dense in the space of open maps between two Knaster continua. Results about the structure of the semigroup of open maps ...

The Lattice of Knaster Continua

Subadditive Ergodic Theorems

Above is the famous Fekete’s lemma which demonstrates that the ratio of subadditive sequence (an) to n tends to a limit as n approaches infinity. This lemma is quite crucial in the field of subadditive ergodic theorems because it gives mathematicians some general ideas and guidelines in the non-random setting and leads to analogous discovery in the random setting. Kingman’s Subadditive Ergodic ...

Homotopy Classes of Maps between Knaster Continua

For each positive integer n, let gn : I → I be defined by the formula gn (t) = v (nt). Observe that gn stretches n times and then folds the resulting interval [0, n] onto [0, 1]. The map g2 is the very well known “roof-top” map. For any two positive integers m and n, gm ◦ gn = gmn. Consequently, gn and gm commute (see, for example, [8, Proposition 2.2]). Let N = {n1, n2, . . . } be a sequence o...