Heteroclinic tangles in time-periodic equations
The authors study the dynamics of heteroclinic tangles, which can be applied to the analysis of various specific differential equations. The authors prove that when a heteroclinic loop is periodically perturbed, three types of heteroclinic tangles appear, namely: transient heteroclinic tangles which do not contain Gibbs measures; heteroclinic tangles dominated by sinks which present stable dynamical behavior; heteroclinic tangles with strange attractors which admit SRB measures representing chaos. Numerical explorations of the dynamics of heteroclinic tangles are presented as well. An application of the theoretical and numerical results is given in the example.
scientific article; zbMATH DE number 6126881