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An investigation of the parameter space for a family of dissipative mappings
Juliano A de Oliveira1, Leonardo T Montero1, Diogo R da Costa2
1Universidade Estadual Paulista (UNESP), Câmpus de São João da Boa Vista, Av. Profa. Isette Corrêa Fontão, 505, 13876-750 SP, Brazil.
Abstract:
The parameter plane investigation for a family of two-dimensional, nonlinear, and area contracting map is made. Several dynamical features in the system such as tangent, period-doubling, pitchfork, and cusp bifurcations were found and discussed together with cascades of period-adding, period-doubling, and the Feigeinbaum scenario. The presence of spring and saddle-area structures allow us to conclude that cubic homoclinic tangencies are present in the system. A set of complex sets such as streets with the same periodicity and the period-adding of spring-areas are observed in the parameter space of the mapping.
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