We consider a class of matrix games in which successful strategies are rewarded by high
reproductive rates, so become more likely to participate in subsequent playings of the game.
Thus, over time, the strategy mix should evolve to some type of optimal or stable state …

When f is a homeomorphisms of the circle S 1 = ~/Z to itself, the rotation number p(f) of f constitutes
an invariant that measures the rate at which the orbit of a point wraps around the circle. The concept
originated with Poincar6 [9] and is best defined in terms of a lift F of f to the real line as …

We study weakly order preserving circle maps with a flat interval, which are differentiable
even on the boundary of the flat interval. We obtain estimates on the Lebesgue measure and
the Hausdorff dimension of the non-wandering set. Also, a sharp transition is found from …

The basic question of this paper is: If you consider two iterated function systems close to one
another in an appropriate topology, are the dimensions of their respective invariant sets
close to one another? It is well-known that the Hausdorff dimension (and Lebesgue …

Let $ F $ be a lift of a homeomorphism $ f:{\Bbb T}^{2}\to {\Bbb T}^{2} $ homotopic to the
identity. We assume that the rotation set $\rho (F) $ is a line segment with irrational slope. In
this paper we use the fact that ${\Bbb T}^ 2$ is necessarily chain transitive under $ f $ if $ f …

These immersions with semi-definite second fundamental forms were studied by M. do
Carmo and E. Lima [2] in the case where M is compact. Their method involves Morse theory
and is not suited for non-compact manifolds. In this paper we present an approach that …

Abstract. Let / be a C° circle map of degree one with precisely one local minimum and one local
maximum, and let [p_(/), p+(/)] be the interval of rotation numbers of/ We study the structure of
the function p(A) = p+(.RA°/), where Rk is the rotation through the angle A … 0. Introduction …

Local scaling of a set means that in a neighborhood of a point the structure of the set can be
mapped into a finer scale structure of the set. These scaling transformations are compact
sets of locally affine (that is: with uniformly $\alpha $-H\" older continuous derivatives) …