Abstract In this paper, we study the persistence, boundedness, convergence, invariance and global asymptotic behavior of positive solutions second-order difference system $$\begin{aligned} x_{n+1}&amp;= \alpha _1 + a e ^{-x_{n-1}} b y_{n} ^{-y_{n-1}},\\ y_{n+1}&amp;= _2 +c ^{-y_{n-1}}+ d x_{n} \quad n=0,1,2,\ldots \end{aligned}$$ <mml:mr...

The presence of positive Lyapunov exponents in a dynamical system is often taken to be equivalent to the chaotic behavior of that system. We construct a Bernoulli toral linked twist map which has positive Lyapunov exponents and local stable and unstable manifolds defined only on a set of measure zero. This is a deterministic dynamical system with the strongest stochastic property, yet it has po...

In this paper, using high order perturbative series expansion method, the critical exponents of the order parameter and susceptibility in transition from ferromagnetic to disordered phases for 1D quantum Ising model in transverse field, with ferromagnetic nearest neighbor and anti-ferromagnetic next to nearest neighbor interactions, are calculated. It is found that for small value of the frustr...

Motivated by a recently developed backward error analysis for QR methods, we consider the error in the Lyapunov exponents of perturbed triangular systems. We consider the case of stable and distinct Lyapunov exponents as well as the case of stable but not necessarily distinct exponents. We illustrate our analytical results with a numerical example. 1. Introduction. Lyapunov exponents are often ...

An efficient and numerically stable method to determine all the Lyapunov characteristic exponents of a dynamical system is developed. Numerical experiments are presented highlighting some aspects of convergence, accuracy and efficiency in the computation of the Lyapunov characteristic exponents.