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Regular version of the site

Article

Stochastic stability of traffic maps

Nonlinearity. 2012. Vol. 25. No. 12. P. 3389-3408.

We study ergodic properties of a family of traffic maps acting in
the space of bi-infinite sequences of real numbers. The corresponding
dynamics mimics the motion of vehicles in a simple traffic flow, which
explains the name. Using connections to topological Markov chains we obtain
nontrivial invariant measures, prove their stochastic stability, and
calculate the topological entropy. Technically these results in the
deterministic setting are related to the construction of measures of maximal
entropy via measures uniformly distributed on periodic points of a given
period, while in the random setting we directly construct (spatially) Markov
invariant measures. In distinction to conventional results the limiting
measures in non-lattice case are non-ergodic. Average velocity of individual
``vehicles'' as a function of their density and its stochastic stability is
studied as well.