Physical and computer experiments involving systems describable by piecewise smooth continuous maps that are nondifferentiable on some surface in phase space exhibit novel types of bifurcations inâ€¦ (More)

Chaotic transients occur in many experiments including those in fluids, in simulations of the plane Couette flow, and in coupled map lattices. These transients are caused by the presence of chaoticâ€¦ (More)

In dynamical systems examples are common in which two or more attractors coexist and in such cases the basin boundary is non-empty. The purpose of this paper is to describe the structure andâ€¦ (More)

Fix a nontrivial interval X C R and let / e C1(X,X) be a chaotic mapping. We denote by Aoo (/) the set of points whose orbits do not converge to a (one-sided) asymptotically stable periodic orbit ofâ€¦ (More)

Physical review. E, Statistical, nonlinear, andâ€¦

2003

We analyze situations where a saddle-node bifurcation occurs on a fractal basin boundary. Specifically, we are interested in what happens when a system parameter is slowly swept in time through theâ€¦ (More)

In dynamical systems examples are common in which two or more attractors coexist, and in such cases the basin boundary is nonempty and the basins often have fractal basin boundaries. The purpose ofâ€¦ (More)

Chaotic transients occur in many experiments including those in fluids, in simulations of the plane Couette flow, and in coupled map lattices and they are a common phenomena in dynamical systems.â€¦ (More)