Irreducible complexity of iterated symmetric bimodal maps

We introduce a tree structure for the iterates of symmetric bimodal maps and identify a subset which we prove to be isomorphic to the family of unimodal maps. This subset is used as a second factor for a $\ast$-product that we define in the space of bimodal kneading sequences. Finally, we give some properties for this product and study the *-product induced on the associated Markov shifts

K-theory for Cuntz-Krieger algebras arising from real quadratic maps

We compute the $K$-groups for the Cuntz-Krieger algebras $\mathcal{O}_{A_{\mathcal{K}(f_{\mu})}}$, where $A_{\mathcal{K}(f_{\mu})}$ is the Markov transition matrix arising from the \textit{kneading sequence }$\mathcal{K} (f_{\mu})$ of the one-parameter family of real quadratic maps $f_{\mu}$.Comment: 8 page

Endogenous Cycles in Optimal Monetary Policy with a Nonlinear Phillips Curve

There is by now a large consensus in modern monetary policy. This consensus has been built upon a dynamic general equilibrium model of optimal monetary policy with sticky prices a la Calvo and forward looking behavior. In this paper we extend this standard model by introducing nonlinearity into the Phillips curve. As the linear Phillips curve may be questioned on theoretical grounds and seems not to be favoured by empirical evidence, a similar procedure has already been undertaken in a series papers over the last few years, e.g., Schaling (1999), Semmler and Zhang (2004), Nobay and Peel (2000), Tambakis (1999), and Dolado et al. (2004). However, these papers were mainly concerned with the analysis of the problem of inflation bias, by deriving an interest rate rule which is nonlinear, leaving the issues of stability and the possible existence of endogenous cycles in such a framework mostly overlooked. Under the specific form of nonlinearity proposed in our paper (which allows for both convexity and concavity and secures closed form solutions), we show that the introduction of a nonlinear Phillips curve into a fully deterministic structure of the standard model produces significant changes to the major conclusions regarding stability and the efficiency of monetary policy in the standard model. We should emphasize the following main results: (i) instead of a unique fixed point we end up with multiple equilibria; (ii) instead of saddle--path stability, for different sets of parameter values we may have saddle stability, totally unstable and chaotic fixed points (endogenous cycles); (iii) for certain degrees of convexity and/or concavity of the Phillips curve, where endogenous fluctuations arise, one is able to encounter various results that seem interesting. Firstly, when the Central Bank pays attention essentially to inflation targeting, the inflation rate may have a lower mean and is certainly less volatile; secondly, for changes in the degree of price stickiness the results are not are clear cut as in the previous case, however, we can also observe that when such stickiness is high the inflation rate tends to display a somewhat larger mean and also higher volatility; and thirdly, it shows that the target values for inflation and the output gap (π^,x^), both crucially affect the dynamics of the economy in terms of average values and volatility of the endogenous variables --- e.g., the higher the target value of the output gap chosen by the Central Bank, the higher is the inflation rate and its volatility --- while in the linear case only the π^ does so (obviously, only affecting in this case the level of the endogenous variables). Moreover, the existence of endogenous cycles due to chaotic motion may raise serious questions about whether the old dictum of monetary policy (that the Central Bank should conduct policy with discretion instead of commitment) is not still very much in the business of monetary policy.Optimal monetary policy, Interest Rate Rules, Nonlinear Phillips Curve, Endogenous Fluctuations and Stabilization

Bowen–Franks groups of reducible bimodal subshifts of finite type

AbstractWe study the Bowen–Franks groups of subshifts of finite type associated with reducible bimodal periodic kneading sequences pairs

Chaotic Dynamics in Optimal Monetary Policy

There is by now a large consensus in modern monetary policy. This consensus has been built upon a dynamic general equilibrium model of optimal monetary policy as developed by, e.g., Goodfriend and King (1997), Clarida et al. (1999), Svensson (1999) and Woodford (2003). In this paper we extend the standard optimal monetary policy model by introducing nonlinearity into the Phillips curve. Under the specific form of nonlinearity proposed in our paper (which allows for convexity and concavity and secures closed form solutions), we show that the introduction of a nonlinear Phillips curve into the structure of the standard model in a discrete time and deterministic framework produces radical changes to the major conclusions regarding stability and the efficiency of monetary policy. We emphasize the following main results: (i) instead of a unique fixed point we end up with multiple equilibria; (ii) instead of saddle--path stability, for different sets of parameter values we may have saddle stability, totally unstable equilibria and chaotic attractors; (iii) for certain degrees of convexity and/or concavity of the Phillips curve, where endogenous fluctuations arise, one is able to encounter various results that seem intuitively correct. Firstly, when the Central Bank pays attention essentially to inflation targeting, the inflation rate has a lower mean and is less volatile; secondly, when the degree of price stickiness is high, the inflation rate displays a larger mean and higher volatility (but this is sensitive to the values given to the parameters of the model); and thirdly, the higher the target value of the output gap chosen by the Central Bank, the higher is the inflation rate and its volatility.Comment: 11 page

A influência da osteoartrose e da artroplastia da anca sobre a atividade laboral em doentes em idade ativa

O impacto da artroplastia total da anca sobre a atividade laboral em doentes jovens com coxartrose é um tema pouco explorado na literatura. Com o objetivo de avaliar a dimensão do problema e reconhecer os fatores clínicos que influenciam o retorno ao emprego nesta população, revimos 81 doentes com uma média etária de 47 anos, submetidos a artroplastia entre 2006 e 2010 (98 ancas). O estudo revelou que antes do procedimento 27 doentes já se encontravam aposentados e que mais 17 se reformaram depois da cirurgia. Os números finais demonstram que apenas 37 dos 81 doentes operados (45,6%) se mantêm a trabalhar depois da intervenção, sendo que o regresso ao trabalho acontece em média 6,7 meses depois da cirurgia. Existem fatores que favorecem positivamente o regresso ao trabalho: sexo masculino, juventude, coxartrose idiopática, prontidão na realização da cirurgia, unilateralidade, hastes metafisárias, postos de chefia e trabalho fisicamente pouco exigente. Apesar da elevada satisfação na resolução dos sintomas conseguido com a artroplastia, existe uma taxa de reforma em idade ativa de 54,4%. Sendo o problema do emprego multifatorial, os médicos sempre tiveram uma palavra sobre o retorno ao trabalho, a qual ainda se encontra baseada na experiência artroplástica do passado. A imergência de novos implantes dotados de maior resistência ao desgaste, aliada ao aprimoramento das técnicas cirúrgicas bem como as condições sociais que se atravessam, devem em nossa opinião introduzir a questão se não será tempo de reformular as restrições medicamente impostas aos pacientes jovens com artroplastia da anca