15 citations · 44 across the 15 of their papers we have counts for
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Intermingled basins: Kan's example on the Riemann sphere
Abbas Fakhari, Ale Jan Homburg, Sebastian van Strien
Kan's discovery of dynamical systems with two attractors whose basins of attraction both have full support, featured specific examples of skew product systems of interval diffeomor…
Intermittent two-point dynamics at the transition to chaos for random circle endomorphisms
Vincent P. H. Goverse, Ale Jan Homburg, Jeroen S. W. Lamb
We establish the existence of intermittent two-point dynamics and infinite stationary measures for a class of random circle endomorphisms with zero Lyapunov exponent, as a dynamica…
Thick attractors with intermingled basins
Abbas Fakhari, Ale Jan Homburg
We construct various novel and elementary examples of dynamics with metric attractors that have intermingled basins. A main ingredient is the introduction of random walks along orb…
Iterated function systems of affine expanding and contracting maps on the unit interval
Ale Jan Homburg, Charlene Kalle
We analyze the two-point motions of iterated function systems on the unit interval generated by expanding and contracting affine maps, where the expansion and contraction rates are…
Symmetric homoclinic tangles in reversible dynamical systems have positive topological entropy
Ale Jan Homburg, Jeroen Lamb, Dmitry Turaev
We consider reversible vector fields in such that the set of fixed points of the involutory reversing symmetry is -dimensional. Let such system have a smooth o…
Critical intermittency in random interval maps
Ale Jan Homburg, Charlene Kalle, Marks Ruziboev +2
Critical intermittency stands for a type of intermittent dynamics in iterated function systems, caused by an interplay of a superstable fixed point and a repelling fixed point. We…