Complete set of invariants for a Bykov attractor

In this paper we consider an attracting heteroclinic cycle made by a 1-dimensional and a 2-dimensional separatrices between two hyperbolic saddles having complex eigenvalues. The basin of the global attractor exhibits historic behaviour and, from the asymptotic properties of these non-converging time averages, we obtain a complete set of invariants under topological conjugacy in a neighborhood of the cycle. These invariants are determined by the quotient of the real parts of the eigenvalues of the equilibria, a linear combination of their imaginary components and also the transition maps between two cross sections on the separatrices.Comment: 23 pages, 4 figure

The fractional volatility model : no-arbitrage, leverage and completeness

When the volatility process is driven by fractional noise one obtains a model which is consistent with the empirical market data. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions of the model are obtained with different leverage behaviors. Here, the no-arbitrage and completeness properties of the models are rigorously studied

Between Husband and Father: Queen Isabel of Lancaster’s crossed loyalties

Isabel of Lancaster became engaged to Afonso V of Portugal when they were both seven years old. Her father was Pedro, the uncle of the infant king and regent of the realm after the forcing out of the qneen rnother Leonor of Aragon. The regency allowed Pedro to favoiir his own lineage. However, when Afonso V took over the governinent, other branches of the roya1 family and the high nobility who felt endangered by Pedro's policy started to turn the king against him. We will show how Isabel negotiated her loyalty both to her husband and to her fatber during the conflict that arose between thern, and how she managed to keep her status and power while honouring her father's memory and protecting the other women of her lineage after thc ignominious death of Pedro in a battle against the king.info:eu-repo/semantics/publishedVersio

As Concepções de Educação Física no Ocidente

A valorização do projecto educativo formal (intencional) sofreu no ocidente algumas transformações, notando-se muito cedo, e apesar da visão dualista sempre marcante, preocupações profundas com a formação integral do Homem. No entanto, o dualismo equilibrado Helénico teve condições históricas para se tornar em dualismo reducionista até à Idade Média, marcando significativamente, e no Renascimento, o início das abordagens científicas ao estudo da motricidade humana. O aprofundamento de áreas como a Educação Física (ginástica) e o Desporto moderno surgem, pois, num período conceptual em que de uma análise empírica e higiénico-terapêutica se vai passando a uma análise mais científica, inicialmente baseada na mecânica e na anatomia, e, à medida que se vão desenrolando os estudos médicos, na fisiologia geral e muscular. Este percurso emerge de uma episteme que gerava aquilo que hoje se costuma denominar como paradigma da modernidade e que, no âmbito da motricidade humana Manuel SÉRGIO (1989) denomina como paradigma cartesiano. A dicotomização corpo-espírito com desvalorização cultural do corpo e o desenvolvimento da ciência espartilhante face ao renascimento de uma visão limitada do conhecimento (conhecimento científico), envolvem movimentos recentes na sua contradição. É nesta transição de paradigma dominante que emerge o desenvolvimento da EF na escolaridade obrigatória

Abundance of infinite switching

A heteroclinic network exhibits infinite switching if each infinite sequence of admissible heteroclinic trajectories may be shadowed. Under a set of checkable hypotheses, we describe a class of vector fields exhibiting abundant switching near a network: there exists a set of initial conditions with positive Lebesgue measure realising infinite switching. The proof relies on the existence of "large" strange attractors in the terminology of Broer, Sim\'o and Tatjer (Nonlinearity, 667--770, 1998) near a heteroclinic tangle unfolding an attracting network containing a two-dimensional heteroclinic connection. For our class of vector fields, any small non-empty open ball of initial conditions realizes infinite switching. We illustrate the theory with a specific one-parameter family of differential equations, for which we are able to characterise its global dynamics for almost all parameters.Comment: 30 pages, 6 figures. arXiv admin note: text overlap with arXiv:2111.0255