Starting from the seminal works by Poincaré [13] and Denjoy [3], a deep theory for the dynamics of circle diffeomorphisms has been developed by many authors [1, 7, 8, 17], and most of the fundamental related problems have been already solved. Quite surprisingly, the case of several commuting diffeomorphisms is rater special, as it was pointed out for the first time by Moser [9] in relation to t...

It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be non-derogatory. Rank-one matrices and diagonalizable matrices are also characterized in terms of the commuting graph.

It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be non-derogatory. Rank-one matrices and diagonalizable matrices are also characterized in terms of the commuting graph.

Let n > 0 be an integer and X be a class of groups. We say that a group G satisfies the condition (X , n) whenever in every subset with n + 1 elements of G there exist distinct elements x, y such that 〈x, y〉 is in X . Let N and A be the classes of nilpotent groups and abelian groups, respectively. Here we prove that: (1) If G is a finite semi-simple group satisfying the condition (N , n), then ...

Let $G$ be a countable monoid and let $A$ an Artinian group (resp. module). $\Sigma \subset A^G$ closed subshift which is also subgroup submodule) of $A^G$. Suppose that $\Gamma$ finitely generated consisting pairwise commuting cellular automata \to \Sigma$ are homomorphisms groups modules) with binary operation given by composition maps. We show the valuation action on $\Sigma$ satisfies natur...

This paper documents a little-noticed feature of US labor markets—very large variation in the labor supply of married women across cities. We focus on cross-city differences in commuting times as a potential explanation for this variation. We start with a model in which commuting times introduce non-convexities into the budget set. Empirical evidence is consistent with the model’s predictions: ...