We show that, for any compact surface, there is a residual (dense Gδ) set of C 1 area preserving diffeomorphisms which either are Anosov or have zero Lyapunov exponents a.e. This result was announced by R. Mañé, but no proof was available. We also show that for any fixed ergodic dynamical system over a compact space, there is a residual set of continuous SL(2, R)-cocycles which either are unifo...

It has been claimed that Lyapunov exponents computed from electroencephalogram or electrocorticogram (ECoG) time series are useful for early prediction of epileptic seizures. We show, by utilizing a paradigmatic chaotic system, that there are two major obstacles that can fundamentally hinder the predictive power of Lyapunov exponents computed from time series: finite-time statistical fluctuatio...

The aim of this paper is to introduce a new hyperchaotic complex Lorenz system. This hyperchaotic complex system is constructed by adding a linear controller to the second equation of the chaotic complex Lorenz system. The new system is a 7-dimensional continuous real autonomous hyperchaotic system. This system has hyperchaotic attractors and quasi-periodic solutions with three zero Lyapunov ex...

Диофантовы экспоненты являются одними из самых простых количественных характеристик, отвечающих за аппроксимационные свойства линейных подпространств евклидова пространства. Данный обзор посвящeн описанию современного состояния раздела теории диофантовых приближений, изучающего диофантовы и соотношения, которым они удовлетворяют. Мы обсуждаем классические экспоненты, возникающие в задаче прибли...

The Scaling Law for the Discrete Kinetic Growth Percolation Model The critical exponent of the total number of finite clusters α is calculated directly without using scaling hypothesis both below and above the percolation threshold pc based on a kinetic growth percolation model in two and three dimensions. Simultaneously, we can calculate other critical exponents β and γ, and show that the scal...

We study the characteristic exponents of the Hamiltonian system of n (≥ 2) point masses m1, . . . , mn freely falling in the vertical half line {q| q ≥ 0} under constant gravitation and colliding with each other and the solid floor q = 0 elastically. This model was introduced and first studied by M. Wojtkowski. Hereby we prove his conjecture: All relevant characteristic (Lyapunov) exponents of ...