We consider traffic dynamics for a network of signalized intersections under fixed time control, where the outflow from every link is constrained to be equal to an autonomous capacity function (and hence fixed-time control) if the queue length is positive and equal to the cumulative inflow otherwise. In spite of the resulting dynamics being nonLipschitz, recent work has shown existence and uniq...

Let X be a metric space with metric p, let f(X)QX be a continuous mapping, and let h(X) ^X be a homeomorphism. For x&X, the s e t 23^-°o/(^) i called the semi-orbit of # under ƒ and the set n£XZh{x) is called the orbit of # under h. For # £ X , the closure of the semi-orbit of x under ƒ is called the semi-orbit-closure of x under ƒ and the closure of the orbit of x under h is called the orbit-c...

We present a semiclassical explanation of the so-called Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral fluctuations in chaotic dynamics. We work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. The asymptotic expansions of both the nonoscillatory and the oscillatory part of the universal spectral correlator ...

We have derived a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences occurring at bifurcations and in the spherical limit, the trace integrals over the action-angle variables were performed using an improved stationary phase method. The resulting semiclassical level density oscillations and shell-correction energies are in g...

We introduce a novel technique to find the asymptotic time behaviour of deterministic systems exhibiting anomalous diffusion. The procedure is tested for various classes of simple but physically relevant 1–D maps and possible relevance of our findings for more complicated problems is briefly discussed. In the last few years the phenomenon of deterministic diffusion has been widely investigated:...

The Wigner time delay of a classically chaotic quantum system can be expressed semiclassically either in terms of pairs of scattering trajectories that enter and leave the system or in terms of the periodic orbits trapped inside the system. We show how these two pictures are related on the semiclassical level. We start from the semiclassical formula with the scattering trajectories and derive f...

Recent work has identified nonlinear deterministic structure in neuronal dynamics using periodic orbit theory. Troublesome in this work were the significant periods of time where no periodic orbits were extracted — “dynamically dark” regions. Tests for periodic orbit structure typically require that the underlying dynamics are differentiable. Since continuity of a mathematical function is a nec...

We derive a generalized Selberg-type zeta function for a smooth de-terministic ow which relates the spectrum of an evolution operator to the periodic orbits of the ow. This relation is a classical analog of the quantum trace formulas and Selberg-type zeta functions.

– The Harper-Hofstadter problem for two-dimensional electron gas with Rashba spin-orbit coupling subject to periodic potential and perpendicular magnetic field is studied analytically and numerically. The butterfly-like energy spectrum, spinor wave functions as well as the spin density and average spin polarization are calculated for actual parameters of semiconductor structure. Our calculation...

We address the problems in applying cycle expansions to bound chaotic systems, caused by e.g. intermittency and incompleteness of the symbolic dynamics. We discuss zeta functions associated with weighted evolution operators and in particular a one-parameter family of weights relevant for the calculation of classical resonance spectra, semiclassical spectra and topological entropy. For bound int...