Internal Dynamics of Intermittency

By examining the behavior of intermittent trajectories near invariant subspaces for the dynamics of flows or maps we introduce and discuss the concept of internal dynamics of an intermittent attractor to an invariant subspace. For a smooth planar mapping, we give examples where the internal dynamics is minimal (as in on–off intermittency), has a single attracting and a single repelling invariant set (as in in–out intermittency) and more complicated but nonetheless typical examples with several isolated invariant sets in the internal dynamics. In particular we discuss and analyze an example of generalized in–out intermittency in which there is one form of ‘in’-dynamics and two of ‘out’–dynamics. We contrast this behavior with another structurally stable example of intermittency, that exhibits non-ergodic intermittency.

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