Highly eccentric hip-hop solutions of the 2N

We show the existence of families of hip-hop solutions in the equal-mass 2N-body problem which are close to highly eccentric planar elliptic homographic motions of 2N bodies plus small perpendicular non-harmonic oscillations. By introducing a parameter ϵ, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small ϵ ≠ 0, the topological transversality persists and Brouwer's fixed point theorem shows the existence of this kind of solutions in the full system

Population structure in a highly pelagic seabird, the Cory's shearwater (Calonectris diomedea): an examination of genetics, morphology and ecology

Increasing evidence suggests oceanic traits may play a key role in the genetic structuring of marine organisms. Whereas genetic breaks in the open ocean are well known in fishes and marine invertebrates, the importance of marine habitat characteristics in seabirds remains less certain. We investigated the role of oceanic transitions versus population genetic processes in driving population differentiation in a highly vagile seabird, the Cory"s shearwater, combining molecular, morphological and ecological data from 27 breeding colonies distributed across the Mediterranean (Calonectris diomedea diomedea) and the Atlantic (C. d. borealis). Genetic and biometric analyses showed a clear differentiation between Atlantic and Mediterranean Cory"s shearwaters. Ringing-recovery data indicated high site fidelity of the species, but we found some cases of dispersal among neighbouring breeding sites (<300 km) and a few long distance movements (>1000 km) within and between each basin. In agreement with this, comparison of phenotypic and genetic data revealed both current and historical dispersal events. Within each region, we did not detect any genetic substructure among archipelagos in the Atlantic, but we found a slight genetic differentiation between western and eastern breeding colonies in the Mediterranean. Accordingly, gene flow estimates suggested substantial dispersal among colonies within basins. Overall, genetic structure of the Cory"s shearwater matches main oceanographic breaks (Almería-Oran Oceanic Front and Siculo-Tunisian Strait), but spatial analyses suggest that patterns of genetic differentiation are better explained by geographic rather than oceanographic distances. In line with previous studies, genetic, phenotypic and ecological evidence supported the separation of Atlantic and Mediterranean forms, suggesting the 2 taxa should be regarded as different species.