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nlin.CD2022★ 2 cited
Unstable dimension variability, heterodimensional cycles, and blenders in the border-collision normal form
P. A. Glendinning, D. J. W. Simpson
Chaotic attractors commonly contain periodic solutions with unstable manifolds of different dimensions. This allows for a zoo of dynamical phenomena not possible for hyperbolic att…
math.DS2022
Normal forms, differentiable conjugacies and elementary bifurcations of maps
Paul A. Glendinning, David J. W. Simpson
We strengthen the standard bifurcation theorems for saddle-node, transcritical, pitchfork, and period-doubling bifurcations of maps. Our new formulation involves adding one or two…