Abstract
In this paper, we consider the existence of homoclinic/heteroclinic recurrent (periodic, almost periodic, almost automorphic, Birkhoff recurrent, Poisson stable) orbits of the system with the following form z˙=g(z)+μh(t,z,μ). We prove that, under certain conditions on h, if μ is sufficiently small, then the equation admits homoclinic/heteroclinic orbits which have the same character of recurrence as the function h. Our approach is based on the Melnikov method. In particular, we construct topological horseshoes.
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