Beyond the 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...

Periodic Orbit Quantization beyond Semiclassics

A quantum generalization of the semiclassical theory of Gutzwiller is given. The new formulation leads to systematic orbit-by-orbit inclusion of higher h̄ contributions to the spectral determinant. We apply the theory to billiard systems, and compare the periodic orbit quantization including the first h̄ contribution to the exact quantum mechanical results. Typeset using REVTEX

Periodic Orbit Theory

Periodic-orbit theory of the blowout bifurcation

This paper presents a theory for characterization of the blowout bifurcation by periodic orbits. Blowout bifurcation in chaotic systems occurs when a chaotic attractor, lying in some symmetric invariant subspace, becomes transversely unstable. We present an analysis and numerical results that indicate that the bifurcation is mediated by changes in the transverse stability of an infinite number ...

Prey-Predator System; Having Stable Periodic Orbit

The study of differential equations is useful in to analyze the possible past or future with help of present information. In this paper, the behavior of solutions has been analyzed around the equilibrium points for Gause model. Finally, some results are worked out to exist the stable periodic orbit for mentioned predator-prey system.