Limit cycles for a class of quintic Z6−\mathbb{Z}_6-equivariant systems without infinite critical points

We analyze the dynamics of a 4-parameter family of planar ordinary differential equations, given by a polynomial of degree 5 that is equivariant under a symmetry of order 6. We obtain the number of limit cycles as a function of the parameters, and provide criteria for proving in some cases uniqueness and hyperbolicity of the limit cycle surrounding either 1, 7 or 13 critical points, the origin being always one of these points. The method used is the reduction of the problem to an Abel equation

Distribution and ecology of parent taxa of pollen lodged within the Latin American Pollen Database

The cornerstone of palaeoecological research, concerned with vegetation dynamics over the recent geological past, is a good understanding of the present-day ecology and distribution of the taxa. This is particularly necessary in areas of high floral diversity such as Latin America. Vegetation reconstructions, based on numerous pollen records, now exist with respect to all major vegetation associations from Latin America. With this ever-increasing number of sedimentary records becoming available, there is a need to collate this information and to provide information concerning ecology and distribution of the taxa concerned. The existing Latin American Pollen Database (LAPD) meets the first of these needs. Information concerning the ecology and distribution of the parent taxa responsible for producing the pollen, presently lodged within the LAPD, is the focus of this paper. The 'dictionary' describes the ecology and distribution of the parent taxa responsible for producing pollen identified within sedimentary records. These descriptions are based on a wide range of literature and extensive discussions with members of the palaeoecological community working in different parts of Latin America investigating a range of different vegetation types.Fil: Marchant, Robert. University of Amsterdam; Países BajosFil: Almeida, Lucía. Universidad Nacional Autónoma de México; MéxicoFil: Behling, Hermann. Center for Tropical Maritime Ecology; AlemaniaFil: Berrio, Juan Carlos. University of Amsterdam; Países BajosFil: Bush, Mark. West University Boulevard; Estados UnidosFil: Cleef, Antoine. University of Amsterdam; Países BajosFil: Duivenvoorden, Joost. University of Amsterdam; Países BajosFil: Kappelle, Maarten. Instituto Nacional de Biodiversidad (INBio); Costa RicaFil: De Oliveira, Paulo. Universidade de Sao Paulo; BrasilFil: de Oliveira, Ary Teixeira. Universidade Federal de Lavras; BrasilFil: Lozano García, Socorro. Universidad Nacional Autónoma de México; MéxicoFil: Hooghiemstra, Henry. University of Amsterdam; Países BajosFil: Ledru, Marie Pierre. Instituto de Geociencias; BrasilFil: Ludlow Wiechers, Beatriz. Universidad Nacional Autónoma de México; MéxicoFil: Markgraf, Vera. University of Colorado; Estados UnidosFil: Mancini, Maria Virginia. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Laboratorio de Paleoecología y Palinología; ArgentinaFil: Paez, Marta Mercedes. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Laboratorio de Paleoecología y Palinología; ArgentinaFil: Prieto, Aldo Raul. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Marinas y Costeras. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Marinas y Costeras; Argentina. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Laboratorio de Paleoecología y Palinología; ArgentinaFil: Rangel, Olando. Universidad Nacional de Colombia; ColombiaFil: Salgado Labouriau, Maria Lea. Universidade do Brasília; Brasi