We discuss the relation between ensemble and time averages for quasistationary states of low-dimensional symplectic maps that present remarkable analogies with similar states detected in many-body long-range-interacting Hamiltonian systems.

Time complexity is associated with sensitive dependence on initial conditions and severe intrinsic predictability limits, in particular, the ‘butterfly effect’ paradigm: an exponential error growth and a corresponding characteristic predictability time. This was believed to be the universal...

In this paper, we construct low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). MIM is based on a formulation of the condition of invariance as an equation, and its solution by Newton iterations. A...

Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann–Gibbs statistics is based on the hypothesis of exponential sensitivity to the initial conditions, mixing and ergodicity in Gibbs...

A two-dimensional earthquake model that consists of a single block resting upon a slowly moving rough surface and connected by two springs to rigid supports is studied. Depending on the elastic anisotropy and the friction force three generic regimes are possible: (i) pure creep; (ii) pure...

A statistical thermodynamic approach of moving particles forming an elastic body is presented which leads to reveal molecular–mechanical properties of classical and nonextensive dynamical systems. We derive the Boltzmann–Gibbs (BG) entropy form and relate it to Newton's law of motion in...

We test for the existence of poverty traps and distribution-dependent growth using a nonlinear dynamic panel data model of household incomes allowing for endogenous attrition. Our estimates for Hungary and Russia in the 1990s reveal significant nonlinearity in the dynamics, consistent with the...

This paper deals with the analytical and graphical representation of the bifurcations appearing from the adjustment dynamics of a 2- player Cournot duopoly, proposed by Puu (1997). We establish admissibility conditions on the initial state of the adjustment dynamics and visualize the dynamics in...