In this paper, using the ideas of Bessi and Mather, we present a simple mechanical system exhibiting Arnold diffusion. This system of a particle in a small periodic potential can be also interpreted as ray propagation in a periodic optical medium with a near-constant index of refraction. Arnold diffusion in this context manifests itself as an arbitrary… (More)
We construct a proper C 2-smooth function on R 4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C 2-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.
The model of a bicycle is a unit segment AB that can move in the plane so that it remains tangent to the trajectory of point A (the rear wheel is fixed on the bicycle frame); the same model describes the hatchet planimeter. The trajectory of the front wheel and the initial position of the bicycle uniquely determine its motion and its terminal position; the… (More)
We consider a ball bouncing off infinitely heavy periodically moving plate in the presence of a potential force. Assuming that the potential equals to a power of the ball's height we present conditions guaranteeing recurrence in the sense that the total energy of almost every trajectory does not go to infinity. 1. Introduction. Consider a point mass falling… (More)
Previous studies focusing on amphetamine (AMPH), methamphetamine (METH) and methylphenidate (MPH) neurotoxicity have almost exclusively been conducted in rodents during the light cycle, which is when most rodents sleep. There are virtually no studies that have simultaneously compared the effects of these three stimulants on body temperature and also… (More)
The main model studied in this paper is a lattice of pendula with a nearest-neighbor coupling. If the coupling is weak, then the system is near-integrable and KAM tori fill most of the phase space. For all KAM trajectories the energy of each pendulum stays within a narrow band for all time. Still, we show that for an arbitrarily weak coupling of a certain… (More)
1. INTRODUCTION: THE PONCELET CLOSURE THEOREM. The Poncelet closure theorem (or Poncelet porism) is a classical result of projective geometry. Given nested ellipses γ and , with γ inside , one plays the following game: starting at a point x on , draw a tangent line to γ until it intersects at point y, repeat the construction , starting with y, and so on.… (More)