Related papers: Lyapunov spectrum for multimodal maps
In this paper we prove a multifractal formalism of Birkhoff averages for interval maps with countably many branches. Furthermore, we prove that under certain regularity assumptions on the potential the Birkhoff spectrum is real analytic.…
This paper consists of variations upon the theme of limiting modular symbols. Topics covered are: an expression of limiting modular symbols as Birkhoff averages on level sets of the Lyapunov exponent of the shift of the continued fraction,…
We consider the Schr\"odinger operator on the real line with a $N\ts N$ matrix valued periodic potential, N>1. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define the Lyapunov…
In this paper we make a detailed numerical comparison between three algorithms for the computation of the full Lyapunov spectrum as well as the associated eigen-vectors of general dynamical systems. They are : (a) the standard method, (b) a…
The spectrum of Lyapunov exponents is powerful tool for the analysis of the complex system dynamics. In the general framework of nonlinear dynamical systems a number of the numerical technics have been developed to obtain the spectrum of…
We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, $\lambda$ and $\lambda^\star$ respectively. We discuss the numerical difficulties that arise in…
We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts. This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of…
Working on strongly irreducible planar self-affine sets satisfying the strong open set condition, we calculate the Birkhoff spectrum of continuous potentials and the Lyapunov spectrum.
This is a survey of known results on estimating the principal Lyapunov exponent of a time-dependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of…
We outline the flexibility program in smooth dynamics, focusing on flexibility of Lyapunov exponents for volume-preserving diffeomorphisms. We prove flexibility results for Anosov diffeomorphisms admitting dominated splittings into…
We consider the Schr\"odinger operator on the real line with a 2x2 matrix valued 1-periodic potential. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define a Lyapunov function which…
For a class of dynamical systems, the cookie-cutter maps, we prove that the Lyapunov spectrum coincides with the map given by the Newton-Raphson method applied to the derivative of the pressure function.
We consider a smooth expanding map g on the circle of degree 2. It is known that the Lyapunov exponent of g with respect to the unique invariant measure that is absolutely continuous with respect to the Lebesgue measure is positive and less…
A conjecture connecting Lyapunov exponents of coupled map lattices and the node theorem is presented. It is based on the analogy between the linear stability analysis of extended chaotic states and the Schr\"odinger problem for a particle…
We present a new method to calculate Lyapunov exponents of rigid diatomic molecules in three dimensions (12N dimensional phase space). The spectra of Lyapunov exponents are obtained for 32 rigid diatomic molecules interacting through the…
We study the Lyapunov spectrum of the ergodic measures of isolated homoclinic classes of $C^1$-generic diffeomorphisms. We show that this spectrum has nonempty interior and that any vector in its interior is the spectrum of some ergodic…
We determine the Lyapunov spectrum and stable manifolds of some stochastic flows on the Poincar\'e group associated to Dudley's relativistic processes.
A method to estimate Lyapunov spectra from spatio-temporal data is presented, which is well-suited to be applied to experimental situations. It allows to characterize the high-dimensional chaotic states, with possibly a large number of…
We study multi-frequency quasiperiodic Schr\"{o}dinger operators on $\mathbb{Z} $. We prove that for a large real analytic potential satisfying certain restrictions the spectrum consists of a single interval. The result is a consequence of…
The problems on the location of the matrix spectrum inside or outside domains bounded by ellipses or parabolas are studied. Special Lyapunov-type equations are connected with these problems. Theorems about the unique solvability of such…