Lyapunov and other spectra : a survey ∗

نویسنده

  • Erik S. Van Vleck
چکیده

Motivated by the basic problem of studying stability of nonautonomous linear systems, different definitions of spectra have been proposed over the years. We review some of these definitions, paying particular attention to how the spectra may be computed. Since the spectra are given by intervals of the real line, one would like to compute the endpoints of these intervals. As it turns out, these endpoints may coincide with the Lyapunov exponents (LEs) of the system. For this reason, we will review computational methods which have been used to approximate the LEs.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Boundary effects in the stepwise structure of the Lyapunov spectra for quasi-one-dimensional systems.

Boundary effects in the stepwise structure of the Lyapunov spectra and corresponding wavelike structure of the Lyapunov vectors are discussed numerically in quasi-one-dimensional systems of many hard disks. Four different types of boundary conditions are constructed by combinations of periodic boundary conditions and hard-wall boundary conditions, and each leads to different stepwise structures...

متن کامل

A New Universality of Lyapunov Spectra in Hamiltonian Systems

A new universality of Lyapunov spectra {λi} is shown for Hamiltonian systems. The universality appears in middle energy regime and is different from another universality which can be reproduced by random matrices in the following two points. One is that the new universality appears in a limited range of large i/N rather than the whole range, where N is degrees of freedom. The other is Lyapunov ...

متن کامل

Chaotic Response and Bifurcation Analysis of a Timoshenko Beam with Backlash Support Subjected to Moving Masses

A simply supported Timoshenko beam with an intermediate backlash is considered. The beam equations of motion are obtained based on the Timoshenko beam theory by including the dynamic effect of a moving mass travelling along the vibrating path. The equations of motion are discretized by using the assumed modes technique and solved using the Runge–Kutta method. The analysis methods employed in...

متن کامل

ماهیت ویژه حالتهای فونون در زنجیرهای شبه تناوبی( نقش شبکه‌های فیبوناچی )

  Using the forced oscillator method (FOM) and the transfer-matrix technique, we numerically investigate the nature of the phonon states and the wave propagation, in the presence of an external force, in the chains composed of Fibonacci lattices of type site, bond and mixing models, as the quasiperiodic systems. Calculating the Lyapunov exponent and the participation ratio, we also study the lo...

متن کامل

Almost Additive Thermodynamic Formalism: Some Recent Developments

This is a survey on recent developments concerning a thermodynamic formalism for almost additive sequences of functions. While the nonadditive thermodynamic formalism applies to much more general sequences, at the present stage of the theory there are no general results concerning for example a variational principle for the topological pressure or the existence of equilibrium or Gibbs measures,...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007