OBJECTIVE:To assess the relative risk for AIDS between men who have sex with other men and heterosexual men. METHODS:Estimates on the proportion of men who have sex with men in Brazil and AIDS data from Brazil's Information System for Notifi able Diseases, were utilized. Estimates were calculated for the relative risk (RR) for AIDS of men who have sex with men with respect to heterosexual masculine population in Brazil; state and city of São Paulo; and state and city of Rio de Janeiro, from 1996 to 2003. The trajectory of the RR in this period was also analyzed. RESULTS:The estimates for relative risk decreased, with a tendency to stabilize: from 34.3 to 19.3 in the entire country and from 32.1 and 6.3 in the locations analyzed. In the country in 2003, the relative risk of bisexual men in relation to heterosexual men was 16.0. The RR for exclusive homosexuals had a decreasing trajectory in all of the locations studied, but not for the bisexual population. CONCLUSIONS:In all locations, the relative risk for men who have sex with other men was higher in relation to heterosexual men. This result indicates a high and persistent vulnerability among this population.

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Abstract. In this paper we give a complete set of invariants (moduli) for mild and strong semilocal equivalence for certain two parameter families of diffeomorphisms on surfaces. These families exhibit a quasi-transversal saddle-connection between a saddle-node and a hyperbolic periodic point. IntroductionGenerically diffeomorphisms with simple recurrence are Morse-Smale and therefore structurally stable [9]. It is conjectured that generically one parameter families of diffeomorphisms, starting at a Morse-Smale one, first bifurcate either by the loss of hyperbolicity of a periodic orbit or by the appearance of a nontransversal saddle-connection [10]. Such one-parameter families may not be stable, but in several relevant cases the classes of equivalence may be parametrized by finitely many real invariants (moduli) as introduced in [8]. To be more precise, let us recall some definitions and results. /. Beloqui and M. J. PacificoA complete characterization of stable generic arcs f^ of diffeomorphisms such that fp is Morse-Smale for /j. <0 and f 0 has simple recurrence was established in [11]. They proved in fact that one of the periodic orbits of/ 0 must be nonhyperbolic and that this orbit is either a saddle-node or a flip. Also, in [11], it is proved that arcs going through either a saddle-node or a flip orbit are strongly stable near these orbits. But arcs passing through a Hopf orbit are not even mildly stable due to the appearance of invariant circles where the restriction of the diffeomorphisms have irrational rotation number. Now, in the same context, if the diffeomorphism at the first point of bifurcation has simple recurrence and all periodic orbits are hyperbolic then their unstable and stable manifolds meet transversally except along one orbit. In this case the arc is not even mildly stable. For instance, let / be a diffeomorphism of a surface which exhibits two hyperbolic fixed points p, q such that W"(p) meets W s (q) along a unique orbit of quasi-transversal intersection (parabolic contact) and let g be near / so that it also exhibits a unique orbit of quasi-transversal intersection between W u (q) and W s (p), where q and p are fixed points for g near q and p. F o r / and g to be equivalent near the closure of this orbit it is necessary and sufficient that log/?"(). For mild equivalence there is one modulus which is A.For one parameter families of vector fields, a complete set of topological invariants near quasi-transversal saddle-connections was established in [14], after the initial contributions of [13] and [1].For generic two-parameter families...

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OBJECTIVE:To assess the relative risk for AIDS between men who have sex with other men and heterosexual men. METHODS:Estimates on the proportion of men who have sex with men in Brazil and AIDS data from Brazil's Information System for Notifi able Diseases, were utilized. Estimates were calculated for the relative risk (RR) for AIDS of men who have sex with men with respect to heterosexual masculine population in Brazil; state and city of São Paulo; and state and city of Rio de Janeiro, from 1996 to 2003. The trajectory of the RR in this period was also analyzed. RESULTS:The estimates for relative risk decreased, with a tendency to stabilize: from 34.3 to 19.3 in the entire country and from 32.1 and 6.3 in the locations analyzed. In the country in 2003, the relative risk of bisexual men in relation to heterosexual men was 16.0. The RR for exclusive homosexuals had a decreasing trajectory in all of the locations studied, but not for the bisexual population. CONCLUSIONS:In all locations, the relative risk for men who have sex with other men was higher in relation to heterosexual men. This result indicates a high and persistent vulnerability among this population.