Periodic orbits and dynamical spectra (Survey)
نویسنده
چکیده
Basic results in the rigorous theory of weighted dynamical zeta functions or dynamically defined generalized Fredholm determinants are presented. Analytic properties of the zeta functions or determinants are related to statistical properties of the dynamics via spectral properties of dynamical transfer operators, acting on Banach spaces of observables.
منابع مشابه
Periodic Orbits in Arithmetical Chaos
1 Length spectra of periodic orbits are investigated for some chaotic dynamical systems whose quantum energy spectra show unexpected statistical properties and for which the notion of arithmetical chaos has been introduced recently. These systems are defined as the uncon-strained motions of particles on two dimensional surfaces of constant negative curvature whose fundamental groups are given b...
متن کاملTime-reversal symmetry in dynamical systems: a survey
In this paper we survey the topic of time-reversal symmetry in dynamical systems. We begin with a brief discussion of the position of time-reversal symmetry in physics. After defining time-reversal symmetry as it applies to dynamical systems, we then introduce a major theme of our survey, namely the relation of time-reversible dynamical sytems to equivariant and Hamiltonian dynamical systems. W...
متن کاملUse of Harmonic Inversion Techniques in Semiclassical Quantization and Analysis of Quantum Spectra
Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and to extract dynamical information from quantum spectra which has been unattainable before, such as bifurcations of orbits, the uncovering of hidden ghost orbi...
متن کاملAnalyzing lyapunov spectra of chaotic dynamical systems
It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory, we derive numerical and in particular, analytical results that provide insights into the overall behavior of the Lyapunov exponents particularly for strange attractors. The corresponding distri...
متن کاملNumerical Continuation of Symmetric Periodic Orbits
The bifurcation theory and numerics of periodic orbits of general dynamical systems is well developed, and in recent years there has been rapid progress in the development of a bifurcation theory for symmetric dynamical systems. But there are hardly any results on the numerical computation of those bifurcations yet. In this paper we show how spatiotemporal symmetries of periodic orbits can be e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998