Connecting orbits in one-parameter families of flows

Abstract

AbstractGiven a family of flows parametrized by an interval and a Morse decomposition which continues across the interval, a procedure is devised to detect connecting orbits at various parameter values. This is done by putting a small drift on the parameter space and considering the flow on the product of the phase space and the parameter interval. The Conley index and connection matrix are used to analyse the flow on the product space, then the drift is allowed to go to zero to obtain information about the original family of flows. This method can be used to detect connections between rest points of the same index for example.