Abstract
We introduce a renormalization scheme to study the asymptotic dynamical behaviour of a family of mechanical systems with non-isochronous potentials with an elliptic equilibrium. This renormalization scheme acts on a family of orbits of these mechanical systems, all of which are contained on neighbourhoods of the elliptic equilibrium, by rescaling space and shifting time in an appropriate way. We present some new results regarding the properties of this renormalization scheme, and examine the strong connection it has with the focal decomposition for the Euler-Lagrange equation of this family of mechanical systems.

Abstract
We consider an international trade economical model where two firms of different countries compete in quantities and can use three different strategies: (i) repealed collusion, (ii) deviation from the foreigner firm followed by punishment by he home country and then followed by repeated Cournot, or (iii) repeated deviation followed by punishment. In some cases (ii) and (iii) can be interpreted as dumping, We compute the profits of both firms for each strategy and we characterize the econc,mical parameters where each strategy is adopted by the firms.

Abstract

Abstract
We introduce a model of tourism choice where we consider that the choice of a tourism resort by a tourist, depends not only on the characteristics of the product offered by the resort but depends also on certain characteristics -crowding types- of the other tourists that have chosen the same resort. To get insights about the effect of crowding types in the allocation of tourists across resorts we exploit a club formation approach and model the framework by means of a Nash game. We establish existence of strategic equilibrium and characterize relevant equilibria.

Abstract
On a symmetric differentiated Stackelberg duopoly model in which there is asymmetric demand information owned by leading and follower firms, we show that the leading firm does not necessarily have advantage over the following one. The reason for this is that the second mover can adjust its output level after observing the realized demand, while the first mover chooses its output level only with the knowledge of demand distribution.

Abstract
In the paper, we discuss two questions about degree d smooth expanding circle maps, with d >= 2. (i) We characterize the sequences of asymptotic length ratios which occur for systems with Holder continuous derivative. The sequences of asymptotic length ratios are precisely those given by a positive Holder continuous function s (solenoid function) on the Cantor set C of d-adic integers satisfying a functional equation called the matching condition. In the case of the 2-adic integer Cantor set, the functional equation is s(2x + 1) = s(x)/s(2x) 1 + 1s(2x-1) -1. We also present a one-to-one correspondence between solenoid functions and affine classes of exponentially fast d-adic tilings of the real line that are fixed points of the d-amalgamation operator. (ii) We calculate the precise maximum possible level of smoothness for a representative of the system, up to diffeomorphic conjugacy, in terms of the functions s and cr(x) = (1 + s(x))/(1 + (s(x + 1))(-1)). For example, in the Lipschitz structure on C determined by s, the maximum smoothness is C1+alpha for 0 < alpha <= 1 if and only if s is alpha-Holder continuous. The maximum smoothness is C2+alpha for 0 < alpha <= 1 if and only if cr is (1 + alpha)-Holder. A curious connection with Mostow type rigidity is provided by the fact that s must be constant if it is alpha-Holder for alpha > 1.