6 papers
Switched flow systems: pseudo billiard dynamics
Michael Blank, Leonid Bunimovich
We study a class of dynamical systems which generalizes and unifies some models arising in the analysis of switched flow systems in manufacturing. General properties of these dynam…
Ergodic properties of a simple deterministic traffic flow model re(al)visited
Michael Blank
We study statistical properties of a family of maps acting in the space of integer valued sequences, which model dynamics of simple deterministic traffic flows. We obtain asymptoti…
Perron-Frobenius spectrum for random maps and its approximation
Michael Blank
To study the convergence to equilibrium in random maps we developed the spectral theory of the corresponding transfer (Perron-Frobenius) operators acting in a certain Banach space…
Dynamics of traffic jams: order and chaos
Michael Blank
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on…
Asymptotically exact spectral estimates for left triangular matrices
Michael Blank
For a family of left triangular matrices with binary entries we derive asymptotically exact (as ) representation for the complete eigenvalues-eigenvectors problem…
Variational principles in the analysis of traffic flows. (Why it is worth to go against the flow.)
Michael Blank
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows…