Model
Digital Document
Publisher
Florida Atlantic University
Description
A geometric model of a reinjected cuspidal horseshoe is constructed, that resembles the
standard horseshoe, but where the set of points that escape are now reinjected and contribute to
richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing
an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from
classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic
topology to show that for suitable parameters the flow contains a strange attractor.
standard horseshoe, but where the set of points that escape are now reinjected and contribute to
richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing
an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from
classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic
topology to show that for suitable parameters the flow contains a strange attractor.
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