138 citations · 240 across the 14 of their papers we have counts for
10 papers · 1 filter
Uncountably many cases of Filippov's sewed focus
Paul Glendinning, S. John Hogan, Martin Homer +2
The sewed focus is one of the singularities of planar piecewise smooth dynamical systems. Defined by Filippov in his book 'Differential Equations with Discontinuous Righthand Sides…
Heterodimensional cycles and noninvertible blenders in piecewise smooth two dimensional maps
Paul Glendinning
Heterodimensional cycles are heteroclinic cycles that connect periodic orbits whose unstable manifolds have different dimensions. This is a source of nonhyperbolic dynamics and uns…
Differentiable conjugacies for one-dimensional maps
P. A. Glendinning, D. J. W. Simpson
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topolo…
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…
Inclusion of higher-order terms in the border-collision normal form: persistence of chaos and applications to power converters
David J. W. Simpson, Paul A. Glendinning
The dynamics near a border-collision bifurcation are approximated to leading order by a continuous, piecewise-linear map. The purpose of this paper is to consider the higher-order…
Chaos in the border-collision normal form: A computer-assisted proof using induced maps and invariant expanding cones
P. A. Glendinning, D. J. W. Simpson
In some maps the existence of an attractor with a positive Lyapunov exponent can be proved by constructing a trapping region in phase space and an invariant expanding cone in tange…