Titlebook: Scaling Laws in Dynamical Systems; Edson Denis Leonel Book 2021 Higher Education Press 2021 Scaling laws in nonlinear systems.Phase transi

ventilate

The Logistic-Like Map,nts and their stability are discussed as well as the convergence to the stationary state at and near at the bifurcations. We show the critical exponents defining the convergence to stationary state for the transcritical and supercritical pitchfork bifurcations are not universal and do depend on the

languid

fetter

A Fermi Accelerator Model,model, also called as Fermi-Ulam model, which is made via a two-dimensional mapping. We discuss how to construct the equations governing the dynamics of the model, the main properties of the phase space including an investigation of the fixed points stability and show that the chaotic sea admits a s

智力高

Dissipation in the Fermi-Ulam Model, inelastic collisions that is when the particle has a fractional loss of energy upon collision. We will show that depending on the control parameters, stable and unstable manifolds obtained from the same saddle fixed point cross each other producing a crisis event. Such a crisis destroys the chaotic

绅士

Localization of Invariant Spanning Curves,ove of the chaotic sea. The idea is to use a transition from local to global chaos observed in the standard mapping to describe the position of the first invariant spanning curve in a family of mappings which the angles diverge in the limit of vanishingly action. The knowledge of the first invariant

一再困扰

啪心儿跳动

Scaling on a Dissipative Standard Mapping,apping, which is explained via the analytical solution of the diffusion equation. It gives the probability of observing a particle with a specific action at a given time. The momenta of the probability are determined and the behavior of the average squared action is obtained. The limits of small and

Pert敏捷

Lumbar-Spine

Time Dependent Billiards,s of the particles considering that the velocity of the particle is given by the application of the momentum conservation law at each impact with the moving boundary. After the collision, the velocity of the particle changes, consequently a new pair of variables is added to the usual pair of angular

STING

Suppression of Fermi Acceleration in the Oval Billiard,ics in the static billiard is a sufficient condition to produce unlimited diffusion in the energy, i.e, Fermi acceleration, when a time perturbation to the boundary is introduced. We show in this chapter that the introduction of a drag force of the type ., or . or . with . and . destroys the unlimit