Explosion of smoothness for conjugacies between multimodal maps

Let $f$ and $g$ be smooth multimodal maps with no periodic attractors and no neutral points. If a topological conjugacy $h$ between $f$ and $g$ is $C^{1}$ at a point in the nearby expanding set of $f$, then $h$ is a smooth diffeomorphism in the basin of attraction of a renormalization interval of $f$. In particular, if $f:I \to I$ and $g:J \to J$ are $C^r$ unimodal maps and $h$ is $C^{1}$ at a boundary of $I$ then $h$ is $C^r$ in $I$.Comment: 22 page

Explosion of smoothness from a point to everywhere for conjugacies between diffeomorphisms on surfaces

For diffeomorphisms on surfaces with basic sets, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point in the basic set then the conjugacy has a smooth extension to the surface. These results generalize the similar ones of D. Sullivan, E. de Faria and ours for one-dimensional expanding dynamics

Anosov Diffeomorphisms and γ -Tilings

We consider a toral Anosov automorphism G γ : T γ → T γ given by G γ (x, y) = (ax+ y, x) in the base, where a∈ N\ { 1 } , γ= 1 / (a+ 1 / (a+ 1 / …)) , v= (γ, 1) and w= (- 1 , γ) in the canonical base of R 2 and T γ = R 2 / (vZ× wZ). We introduce the notion of γ-tilings to prove the existence of a one-to-one correspondence between (i) marked smooth conjugacy classes of Anosov diffeomorphisms, with invariant measures absolutely continuous with respect to the Lebesgue measure, that are in the isotopy class of G γ ; (ii) affine classes of γ-tilings; and (iii) γ-solenoid functions. Solenoid functions provide a parametrization of the infinite dimensional space of the mathematical objects described in these equivalences.info:eu-repo/semantics/publishedVersio

Tilings and Anosov diffeomorphisms

A. Pinto and D. Sullivan [4] proved a one-to-one correspondence between: (i) C1+ conjugacy classes of expanding circle maps; (ii) solenoid functions and (iii) Pinto-Sullivan’s dyadic tilings on the real line. A. Pinto [1,3] introduced the notion of golden tilings and proved a one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, that are topologically conjugate to the linear automorphism G(x; y) = (x + y; x), (ii) affine classes of golden tilings and (iii) solenoid functions. Here we extend this last result and we exhibit a natural one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, that are topologically conjugate to the linear automorphism G(x; y) = (ax+y; ax), where a 2 N, (ii) affine classes of tilings in the real line and (iii) solenoid functions. The solenoid functions give a parametrization of the infinite dimensional space consisting of the mathematical objects described in the above equivalences

Golden tilings

In this talk we present the definition of a golden sequence {ri}i2N. These golden sequences have the property of being Fibonacci quasi-periodic and determine a tiling in the real line. We prove a one-to-one correspondence between: (i) affine classes of golden tilings; (ii) smooth conjugacy classes of Anosov difeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, that are topologically conjugate to the Anosov automorphis

Golden tilings

A. Pinto and D. Sullivan [3] proved a one-to-one correspondence between: (i) Cl+ conjugacy classes of expanding circle maps; (ii) solenoid functions and (iii) Pinto-Sullivan's dyadic tilings on the real line. Here, we prove a one-to-one correspondence between: (i) golden tilings; (ii) smooth conjugacy classes of golden diffeomorphism of the circle that are fixed points of renormalization; (iii) smooth conjugacy classes of Anosov difeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, that are topologically conjugated to the Anosov automorphism G(x, y) = (x + y, x) and (iv) solenoid functions

Renormalization of circle diffeomorphism sequences and markov sequences

We show a one-to-one correspondence between circle diffeomorphism sequences that are C^{ 1+n}-periodic points of renormalization and smooth Markov sequences.We thank the financial support of LIAAD–INESC TEC through program PEst, USP-UP project, Faculty of Sciences, University of Porto, Calouste Gulbenkian Foundation, FEDER and COMPETE Programmes, PTDC/MAT/121107/2010 and Fundação para a Ciência e a Tecnologia (FCT). J. P.Almeida acknowledges the FCT support given through Grant SFRH/PROTEC/49754/2009

Ladrilhamentos dourados da recta real

Apresentaremos a definição de sucessão dourada {r_i}. Estas sucessões possuem a propriedade de serem Fibonacci quasi-periodicas e determinam um ladrilhamento na recta real. Provaremos uma correspondência bijectiva entre: (i) sucessões douradas; (ii) Classes de conjugação diferenciáveis de difeomorfismos de Anosov na classe de conjugação topológica do automorfismo hiperbólico do toro G(x,y) =(x+y,x); (iii) Classes de conjugação diferenciáveis de difeomorfismos da circunferência com número de rotação igual ao inverso do número de ouro e que são pontos fixos do operador renormalização

Polymerase chain reaction for the direct detection of Brucella spp. in milk and cheese.

A polymerase chain reaction test was developed to detect Brucella spp. directly in milk and cheese and optimized using primers for the BSCP-31 gene. A total of 46 cheese samples produced with sheep and goats milk were assayed, and Brucella spp. was detected in 46% of them, especially in cheese made from sheep milk. This method is of remarkable epidemiologic interest because it is an indirect test indicating the sanitary quality of milk used in dairy industries. The method showed good sensitivity and specificity. It is faster and less expensive than the conventional bacteriological assays

R&D dynamics with asymmetric efficiency

We consider an R&D investment function in a Cournot duopoly competition model inspired in the logistic equation. We study the economical effects resulting from the firms having different R&D efficiencies. We present three cases: (1) both firms are efficient and have the same degree of efficiency; (2) both firms are less efficient and have the same degree of efficiency; (3) firms are asymmetric in terms of the efficiency of their R&D investment programs. We study the myopic dynamics on the production costs obtained from investing the Nash investment equilibria.info:eu-repo/semantics/publishedVersio