Orbit Theory

Periodic Orbit Theory

Beyond the periodic orbit theory

The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated Fredholm determinants are of particularly simple polynomial form. The theory developed suggests an alternative to the conventional periodic orbit theory appr...

Orbit Equivalence and Measured Group Theory

We give a survey of various recent developments in orbit equivalence and measured group theory. This subject aims at studying infinite countable groups through their measure preserving actions. 2000 Mathematical Subject Classification: Primary 37A20; Secondary 46L10; 28D15.

Periodic orbit theory of strongly anomalous transport

We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical appearance of phase transitions in the spectrum of transport exponents is explained. PACS numbers: 05.45.-a † also at Istituto Nazionale Fisica Nucleare, Se...

Spin-Orbit Interaction from Matrix Theory

We study the leading order spin dependence of graviton scattering in eleven dimensions, and show that the results obtained from supergravity and from Matrix Theory precisely agree. 1 Work supported in part by DOE grant DE-FG03-92-ER40701.