Abstract
Given a hyperbolic invariant set of a diffeomorphism on a surface, it is proved that, if the holonomies are sufficiently smooth, then the diffeomorphism on the hyperbolic invariant set is rigid in the sense that it is C1+ conjugate to a hyperbolic affine model.

Abstract
We present an infinite dimensional space of C1+ smooth conjugacy classes of circle diffeomorphisms that are C1+ fixed points of renormalization. We exhibit a one-to-one correspondence between these C1+ fixed points of renormalization and C1+ conjugacy classes of Anosov diffeomorphisms.

Abstract
We present a tourism model where the choice of a resort by a tourist depends not only on the product offered in the resort, but also on the characteristics of the other tourists staying in the resort. In order to explore the effect of the types of the tourists in the allocation of tourists across resorts, we introduce a game theoretical model and describe the relevant Nash equilibria.

Abstract
We consider a price competition in a duopoly with substitutable goods, linear and symmetric demand. There is a firm (F-1) that chooses first the price p(1) of its good; the other firm (F-2) observes p(1) and then chooses the price p(2) of its good. The conclusions of this price-setting dynamical duopoly are substantially altered by the presence of either differentiated goods or asymmetric information about rival's production costs. In this paper, we consider asymmetric information about rival's production costs. We do ex-ante and ex-post analyses of firms' profits and market prices. We compare the ex-ante firms' expected profits with the ex-post firms' profits.

Abstract
The conclusions of the Bertrand model of competition are substantially altered by the presence of either differentiated goods or asymmetric information about rival's production costs. In this paper, we consider a Bertrand competition, with differentiated goods. Furthermore, we suppose that each firm has two different technologies, and uses one of them according to a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We show that this game has exactly one Bayesian Nash equilibrium. We do ex-ante and ex-post analyses of firms' profits and market prices. We prove that the expected profit of each firm increases with the variance of its production costs. We also show that the expected price of each good increases with both expected production costs, being the effect of the expected production costs of the rival dominated by the effect of the own expected production costs.

Abstract
We describe three different but related scenarios for determination of asset prices in an incomplete market: one scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing considerations.