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math.DS2022
Border-collision bifurcations from stable fixed points to any number of coexisting chaotic attractors
David J. W. Simpson
In diverse physical systems stable oscillatory solutions devolve into more complicated dynamical behaviour through border-collision bifurcations. Mathematically these occur when a…
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…