Admissible Hierachic Sets

In this paper we present a solution concept for abstract systems called the admissible hierarchic set. The solution we propose is a refinement of the hierarchic solution, a generalization of the von Neumann and Morgenstern solution. For finite abstract systems we show that the admissible hierarchic sets and the von Neumann and Morgenstern stable sets are the only outcomes of a coalition formation procedure (Wilson, 1972 and Roth, 1984). For coalitional games we prove that the core is either a vN&M stable set or an admissible hierarchic set.abstract system, coalitional game, corem, hierarchic solution, subsolution, Von Neumann and Morgenstern stable set

A (short) survey on Dominated Splitting

We present here the concept of Dominated Splitting and give an account of some important results on its dynamics.Comment: 19 page

Dominated Pesin theory: convex sum of hyperbolic measures

In the uniformly hyperbolic setting it is well known that the set of all measures supported on periodic orbits is dense in the convex space of all invariant measures. In this paper we consider the converse question, in the non-uniformly hyperbolic setting: assuming that some ergodic measure converges to a convex combination of hyperbolic ergodic measures, what can we deduce about the initial measures? To every hyperbolic measure $\mu$ whose stable/unstable Oseledets splitting is dominated we associate canonically a unique class $H(\mu)$ of periodic orbits for the homoclinic relation, called its \emph{intersection class}. In a dominated setting, we prove that a measure for which almost every measure in its ergodic decomposition is hyperbolic with the same index such as the dominated splitting is accumulated by ergodic measures if, and only if, almost all such ergodic measures have a common intersection class. We provide examples which indicate the importance of the domination assumption.Comment: final version, new co-author, to appear in: Israel Journal of Mathematic