Symbolic Plane Research Articles

A Identidade Judaica: Uma Identidade Religiosa?

A identidade judaica é discutida à luz do conceito de identidade social da Escola de Bristol (Tajfel, 1972), a partir da pergunta sobre se é possível conceber um judaísmo sem religião. A vida de Sigmund Freud, neste sentido, é emblemática, uma vez que o grande mestre da Psicanálise declara-se, durante muitos anos, cidadão austríaco admirador da cultura almã,ó chegando a se assumir como judeu só depois da ascensão do nazismo.

Experimental identification of chaotic fibers

In a 2D parameter space, by using nine experimental time series of a Chua’s circuit, we characterized three codimension-1 chaotic fibers parallel to a period-3 window. To show the local preservation of the properties of the chaotic attractors in each fiber, we applied the closed return technique and two distinct topological methods. With the first topological method we calculated the linking numbers in the sets of unstable periodic orbits, and with the second one we obtained the symbolic planes and the topological entropies by applying symbolic dynamic analysis.

Evolution of chaos in the Matsumoto-Chua circuit: a symbolic dynamics approach

We use symbolic dynamics to follow the evolution of the Matsumoto-Chua circuit in the chaotic regime. We consider the evolution of the whole population of unstable periodic orbits and of the associated trajectories, in four chaotic attractors generated by the circuit. Symbolic planes and first return maps are built for different values of the control parameter. The bifurcation mechanism suggests the possibility of the existence of a homoclinic orbit.

Erotic Paranoia and Wife Murder in Calderonian Drama

Calderon's three famous wife-murder plays El medico de su honra, A secreto agravio, secreta venganza and El pintor de su deshonra dramatize the predicament of the husbands who believe they have been dishonored through adulterous acts committed by their wives, who are consequently killed. In each case the marriage is an arranged one, contracted after the death or departure of the wife's former suitor, who then returns to pursue her. Although all three wives remain faithful, they often act precipitously and unwisely, inducing their husbands to believe that their suspicions are justified. In two cases the suitor is killed alongside the wife; the third lover is a royal personage and therefore immune (McKendrick, Theatre, 147). In El medico de su honra only the object of desire, Mencia, is murdered, whereas Enrique, her suitor, escapes punishment because he is the king's brother. In A secreto agravio, secreta venganza and El pintor de su deshonra both the subjects and objects of the illicit, adulterous desire, the lovers and the wives, are punished by the jealous husbands. fact that wife-murders were actually no more frequent in seventeenth-century Spain than elsewhere in Europe, and that their depiction should consequently not be taken as evidence that they were, has led McKendrick to conclude that the idea that the mere suspicion of a wife's or daughter's guilt should lead to bloodshed is a theatrical device; so too is the risk-laden avenging of a secret dishonor (Honour/Vengeance, 317). There were very few recorded cases of wife-murder in the sixteenth as well as the seventeenth century, and, in fact, violence was far more frequently directed outside the family than within it (Stone 77). honor/vengeance code needs to be viewed as a dramatic convention which signifies on a symbolic plane; it expresses anxieties linked to a loss of self-control and rationality: The honour code by its rationalizations protected man from those passions of love and jealousy alien to the self-respecting, self-controlled individual (McKendrick, Honour/Vengeance, 333). sacrifice of an innocent wife can thus be understood as a desperate attempt to redraw boundaries which have been blurred through the dangerous supplement, the desire which exceeds the heterosexual contract of marriage, and to re-gain the control which has been lost. By charting a radically different ideology of sexuality and desire for the Early Modern period, it will be possible to analyze the deeper motivations and anxieties that induce the husbands to murder their wives beside the more obvious ones. Adultery was a far from private issue in Early Modern Europe, and preoccupied social and political institutions alike. church officially viewed adultery as a mortal sin, regardless of whether it was committed by the husband or the wife. In practice, however, a double standard existed owing to the fact that an adulterous woman threatened the principles on which the perpetuation of property was based, whereas an adulterous man left his home unscathed. In countries such as Spain, where criminal codes were based on Roman law, an adulterous woman could be killed by her husband on the spot without his incurring the charge of murder, providing there were witnesses and the wife was caught in flagrante delicto. A woman, however, had no recourse to the law if her husband had a concubine; she was expected to tolerate her husband's extra-marital sexual activities (Hufton 56-7). In England, a wife's murder of her husband was classed as petty treason. husband fulfilled the role of king within the household and his murder was equated with the destruction of sovereign power and the subversion of a God-ordained order. In Early Modern Europe, monogamous marriage was regarded as the institution at the heart of the social system, and this English characterization of the murder of a husband as petty treason suggests that the correspondence between husband and king was more than pure analogy. …

Hénon-like attractor in air bubble formation

We studied the formation of air bubbles in a submerged nozzle in a water/glycerol solution inside a cylindrical tube, submitted to a sound wave perturbation. It was observed a route to chaos via period doubling as a function of the sound wave amplitude. We applied metrical as well as topological characterization to some chaotic attractors. We localized a flip saddle, and we also could establish relations to a Hénon-like dynamics with the construction of symbolic planes.

Politics of pension sharing in urban South Africa

Analysing the practice of pension sharing, this article looks at social and cultural dimensions of ageing in an urban African residential area, Cape Town's Khayelitsha. First, the paper discusses pension sharing as a future-oriented security strategy. Many older Africans in Khayelitsha believe that if they do not share their pensions with their kin, they do not have much chance of being helped in times of need. Pension sharing as an instrumental act is rooted in the perceived underdevelopment of the state social security system on the one hand, and in the very character of African kinship and the fluidity of today's urban domestic units on the other. Partly triggered by poverty and mass unemployment, African pensioners are under severe normative pressure to share their grants within their families. Taking into account African notions of old age and of personhood, and considering the widespread devaluation of older Africans in social constructions, pension sharing provides older Africans with an (easily available) means by which they can earn (self-)respect. Further, state policies indirectly enhance the normative pressure on pensioners to share their old-age pensions. On a symbolic plane the practice may be construed as a political model that conceptualises duty as the inner bond of the social world. In conclusion, it is propounded that the concept of (intergenerational) reciprocity is inadequate to account for pension sharing or practical provision of old-age care.

Masking Gender: A German Carnival Custom in Its Social Context

his essay on Carnivals, Carnival, and Carnivalization this issue, Daniel Crowley observes that astonishing characteristic of Carnival is its conservation of form a situation designed to maximize innovation and creativity. Despite staggering variety of costumes, customs, displays, dramas, and forms of organization found Carnival celebrations over six continents, festival ultimately consists of, as Crowley puts it, such a narrow set of themes! Among this small number of recurrent themes, surely none is more essential to idea of carnivalesque than what Crowley calls reversal phenomenon, Carnival upside-down, which status, age, wealth, and, most prominently, gender get turned on their heads (Babcock 1978). It should come as little surprise that gender, a basic organizing principle all human societies, figures so centrally a festival which, wherever it occurs, involves temporarily inverting social norms. -The most notorious yet long-lived Carnival tradition, suggests Reid Mitchell, was that of cross-dressing (Mitchell 1995: 135). V.V. Ivanov also notes that the inversion of binary male/female.. appears to be a determining factor a significant number of carnival rites involving status reversal. those areas of Western Europe where ancient carnival tradition has been preserved, donning of masks of opposite sex by carnival participants remains salient feature of ritual.... Ivanov concludes that the archetype explaining establishment of these rituals [of transvestism] and their continued practice (in both ritual and nonritual, ordinary behavior) is apparently universal (Ivanov 1984: 12, 13). The symbolic play with gender norms found Carnival is one reason those scholars Crowley dubs have found concept of carnivalesque so appealing and fruitful. Yet despite interest carnivalesque gender inversions, surprisingly little ethnographic research has focused on division of participatory roles between men and women, and relationship of these roles to representations of gender within specific Carnival traditions. Instead, many of post-modern scholars who have reinvigorated study of carnivalesque prefer to read gender inversions on a symbolic plane and then, perhaps, generalize about their social significance, rather than other way around. For instance, Ivanovl cites numerous examples to ascertain that in contemporary ethnology, transvestism (as other carnival rituals) is considered to be an instance of a ritual neutralization of semiotically significant oppositions, this case male/female (Ivanov 1984: 14). But Ivanov offers little information about men and women actually engaging this transvestism, or their conventional positions within their own societies, and instead uses insight about semiotic mediation of binary oppositions to interpret selected literary works. his study of Brazilian Carnival, Roberto DaMatta observes that opposition between street and house is basic, and it can be a powerful tool analyzing Brazilian social world (DaMatta 1991 [1979]: 64). Clearly this symbolic dichotomy is deeply invested matters of gender roles and representations: In house relationships are ruled by 'natural' hierarchies of sex and age... (DaMatta 64). Yet DaMatta remains on level of symbolic generalization, and barely touches on gender at either social or symbolic level; he does, however, briefly conclude that the women of Carnival parade as whores, high up on platforms where they draw attention of everyone's eyes, or around tables and boxes of ballroom where they stir passions (DaMatta 108). Presumably women would disagree with at least portions of this characterization. At DaMatta's personal invitation, Victor Turnerwhom Crowley boasts of not mentioning his paper-also turned his attention to Carnival of Rio. …

Topological Analysis of the EBL Model for the Chaotic NMR Laser**The project supported partially by National Natural Science Foundation of China

By determining relative rotation rates of the extended Bloch-type model, a consistent topological description for the model and the chaotic NMR laser at the parameter regime investigated is indicated. A geometrical method for calculating relative rotation rates, which is different from that of constructing the template, is proposed by establishing a symbolic plane in terms of the ordering of forward and backward sequences encoding unstable periodic orbits.

Symbolic dynamics and periodic orbits for the cardioid billiard

The periodic orbits of the strongly chaotic cardioid billiard are studied by introducing a binary symbolic dynamics. The corresponding partition is mapped to a topological well-ordered symbol plane. In the symbol plane the pruning front is obtained from orbits running either into or through the cusp. We show that all periodic orbits correspond to maxima of the Lagrangian and give a complete list up to code length 15. The symmetry reduction is done on the level of the symbol sequences and the periodic orbits are classified using symmetry lines. We show that there exists an infinite number of families of periodic orbits accumulating in length and that all other families of geometrically short periodic orbits eventually get pruned. All these orbits are related to finite orbits starting and ending in the cusp. We obtain an analytical estimate of the Kolmogorov-Sinai entropy and find good agreement with the numerically calculated value and the one obtained by averaging periodic orbits. Furthermore the statistical properties of periodic orbits are investigated.

The Symbolic Plane and its Secularization in the Spiritual World of Gershom Scholem

The Symbolic Plane and its Secularization in the Spiritual World of Gershom Scholem

Symbolic dynamics. I. Finite dispersive billiards

Orbits in different dispersive billiards systems, for example the three-disk system, are mapped into a topological well-ordered symbolic plane and it is showed that forbidden and allowed orbits are separated by a monotone pruning front. The pruning front can be approximated by a sequence of finite symbolic dynamics grammars.

Periodic orbits in a two-variable coupled map.

Periodic orbits are calculated for a linear transformation composed of two coupled tent maps using a symbolic dynamics defined as the direct product of the single-map symbols {0,1,2}. As the coupling strength is increased orbits are pruned and a crossover to one-dimensional behavior is observed. The disallowed binary orbits containing only symbols {0,1} form a connected region in a binary symbol plane. Stable orbits may appear for strong couplings.

Pruning of orbits in four-disk and hyperbola billiards.

It is shown that for the four-disk system and the hyperbola billiard it is possible to construct a new symbolic plane preserving the orientation existing in the dynamical space. Physical orbits are mapped into the topological well-ordered plane and it is shown that the forbidden and allowed orbits are separated by a monotone pruning front.

Topological and metric properties of Hénon-type strange attractors.

We use the set of all periodic points of H\'enon-type mappings to develop a theory of the topological and metric properties of their attractors. The topology of a H\'enon-type attractor is conveniently represented by a two-dimensional symbol plane, with the allowed and disallowed orbits cleanly separated by the ``pruning front.'' The pruning front is a function discontinuous on every binary rational number, but for maps with finite dissipation \ensuremath{\Vert}b\ensuremath{\Vert}l1, it is well approximated by a few steps, or, in the symbolic dynamics language, by a finite grammar. Thus equipped with the complete list of allowed periodic points, we reconstruct (to resolution of order ${b}^{n}$) the physical attractor by piecing together the linearized neighborhoods of all periodic points of cycle length n. We use this representation to compute the singularity spectrum f(\ensuremath{\alpha}). The description in terms of periodic points works very well in the ``hyperbolic phase,'' for \ensuremath{\alpha} larger than some ${\ensuremath{\alpha}}_{c}$, where ${\ensuremath{\alpha}}_{c}$ is the value of \ensuremath{\alpha} corresponding to the (conjectured) phase transition.