title: Universal Dichotomy for Dynamical Systems with Variable Delay.
abstract: We show that the dynamics of systems with a time-dependent delay is fundamentally affected by the functional form of the retarded argument. Associating with the latter an iterated map, the access map, and a corresponding Koopman operator, we identify two universality classes. Members in the first are equivalent to systems with a constant delay. The new, second class is characterized by the mode-locking behavior of their access maps and by an asymptotically linear, instead of a logarithmic, scaling of the Lyapunov spectrum. The membership depends in a fractal manner only on the parameters of the delay.
authors.affiliation: Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany.
authors.forename: Andreas
authors.initials: A
authors.lastname: Otto
authors.affiliation: Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany.
authors.forename: David
authors.initials: D
authors.lastname: Müller
authors.affiliation: Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany.
authors.forename: Günter
authors.initials: G
authors.lastname: Radons