Homoclinic Bifurcations innDimensions

摘要

Bifurcations near homoclinic orbits inndimensions are described. Depending on the eigenvalues of the Jacobian at the fixed point whose real parts are closest to zero, a strange invariant set of periodic and aperiodic orbits can be produced, which can be described by a Bernoulli shift on a finite set of symbols. These results generalize earlier ones of Shil'nikov, Gaspard, Tresser, Glendinning, and Sparrow, amongst others.