Dynamical properties of a dissipative hybrid Fermi-Ulam-bouncer model

Abstract

Some consequences of dissipation are studied for a classical particle suffering inelastic collisions in the hybrid Fermi-Ulam bouncer model. The dynamics of the model is described by a twodimensional nonlinear area-contracting map. In the limit of weak and moderate dissipation we report the occurrence of crisis and in the limit of high dissipation the model presents doubling bifurcation cascades. Moreover, we show a phenomena of annihilation by pairs of fixed points as the dissipation varies. Specifically, we characterize events of the crisis as the damping coefficients are varied. Moreover, in the limit of high dissipation the system exhibits a sequence of doubling bifurcation cascade. We also report the annihilation of pairs of fixed points as the damping coefficients are varied.

Fermi acceleration and scaling properties of a time dependent oval billiard

“…For the case of D =1 ͑one-dimensional case͒ there are many results concerning the description of Fermi acceleration and the three basic models are ͑i͒ Fermi-Ulam model, [2][3][4][5] ͑ii͒ the bouncer model, [6][7][8][9][10] and ͑iii͒ the hybrid Fermi-Ulam-bouncer model. [11][12][13] Case ͑i͒ consists of a classical particle of mass m, which is confined to bounce between two walls where one of them is fixed and the other one is periodically moving. It is known that for a sinusoidal motion in time of the moving wall, unlimited energy growth is not expected to be observed.…”

An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action

“…with ζ constant recovers the hybrid Fermi-Ulam bouncer model [21,22,23]; -K(I n+1 ) = I n+1 + ζI 2 n+1 recovers the logistic twist mapping [24]. Our goal in this paper is to investigate the dynamical properties for chaotic orbits considering a family of mappings described by h(θ n , I n+1 ) = sin(θ n ) and K = 1/|I n+1 | γ with γ > 0 and p(θ n , I n+1 ) = 0, leading to…”

Survival probability for chaotic particles in a set of area preserving maps

“…Without losing generality, for a wide class of systems the function p is considered p(θ n , J n+1 ) = constant which we will consider it as fixed p(θ n , J n+1 ) = 0 from now on and hence F is varied. The systems within the scope of the general two dimensional map include, the logistic twist mapping [14], the Taylor-Chirikov map [15], Fermi-Ulam accelerator model [16,17], Fermi-Pustylnikov accelerator [18] or bouncer model and Hybrid-Fermi-Ulam-bouncer model [19,20]. In this work, our main goal is to investigate the dynamical properties for an ensemble of particles considering the following expression…”