We study the phenomenon of unlimited energy growth for a classical particle moving in the annular billiard. The model is considered under two different geometrical situations: static and breathing boundaries. We show that when the dynamics is chaotic for the static case, the introduction of a time-dependent perturbation allows that the particle experiences the phenomenon of Fermi acceleration even when the oscillations are periodic.

Several species of Leishmania spp. cause diseases in humans that range from self-healing cutaneous lesions to fatal visceral leishmaniosis. It has been observed that besides being transmitted by sand flies, Leishmania spp. may also be transmitted by arthropods such as ticks and fleas. To investigate the possible role of dog fleas in the transmission of Leishmania spp., Ctenocefalides felis were removed from 22 dogs which were positive according to ELISA and rK-39 tests. A C. felis sample from each of the 22 dogs was used to infect a hamster. The 22 hamsters were euthanized 4 months after infection with the fleas and the blood was subjected to ELISA to detect antibody anti-Leishmania spp., and the spleen samples were submitted to PCR for detection of Leishmania spp. DNA. PCR and ELISA were both positive in 18.1% (4/22), with PCR alone being positive in 45% (10/22) and ELISA alone in only 9% (2/22). These results suggest the participation of dog fleas in the Leishmania spp. cycle. Confirmation that C. felis indeed transmit leishmaniosis to dogs requires new strategies against leishmaniosis to be enforced by public health authorities and which focus on better ways to keep dogs free of fleas.

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Some properties of the annular billiard under the presence of weak dissipation are studied. We show, in a dissipative system, that the average energy of a particle acquires higher values than its average energy of the conservative case. The creation of attractors, associated with a chaotic dynamics in the conservative regime, both in appropriated regions of the phase space, constitute a generic mechanism to increase the average energy of dynamical systems.