Chaos is a general phenomenon in nonlinear dynamical systems. Accelerators { storage rings in particular { in which particles are stored for 10 revolutions constitute a particularly intricate nonlinear dynamical system. (In comparison, the earth has revolved around the sun for only 10 turns.) Storage rings therefore provide an ideal testing ground for chaos physics. In fact, it is the chaos phe...

Crutchfield et al. observed that noise truncates period-doubling cascade and induces chaos. To date, however, very little low-dimensional chaos has been unambiguously identified experimentally. This discrepancy stimulates us to reexamine the noisy logistic map. We find that noise can indeed induce chaos. However, this is not associated with the main 2n cascade. We identify three basic condition...

We argue that transient chaos in deterministic dynamical systems is a major source of noiseinduced chaos. The line of arguments is based on the fractal properties of the dynamical invariant sets responsible for transient chaos, which were not taken into account in previous works. We point out that noise-induced chaos is a weak noise phenomenon since intermediate noise strengths destroy fractali...

Chaos is a general phenomenon in nonlinear dynamical systems. Accelerators { storage rings in particular { in which particles are stored for 10 revolutions constitute a particularly intricate nonlinear dynamical system. (In comparison, the earth has revolved around the sun for only 10 turns.) Storage rings therefore provide an ideal testing ground for chaos physics. In fact, it is the chaos phe...

Chaos criterion for quantum field theory is proposed. Its correspondence with classical chaos criterion in semi-classical regime is shown. It is demonstrated for real scalar field that proposed chaos criterion can be used to investigate stability of classical solutions of field equations. Phenomenon of chaos attracts much attention in various fields of physics. Originally it was associated with...

A complex high-dimensional chaotic behavior, phase chaos, is found in the finite-dimensional Kuramoto model of coupled phase oscillators. This type of chaos is characterized by half of the spectrum of Lyapunov exponents being positive and the Lyapunov dimension equaling almost the total system dimension. Intriguingly, the strongest phase chaos occurs for intermediate-size ensembles. Phase chaos...

We report on an experimental observation of optical wave chaos in a resonator consisting of three standard, high-reflectivity mirrors. The nonseparability of the wave equation necessary for chaos is introduced by violating the paraxial approximation. Until recently progress in optical wave chaos was hampered by the inherent difficulty in realizing suitable microscopic systems; now this novel, m...