Periodic solutions to symmetric Newtonian systems in neighborhoods of orbits of equilibria

Periodic solutions of radially symmetric perturbations of Newtonian systems

The classical Newton equation for the motion of a body in a gravitational central field is here modified in order to include periodic central forces. We prove that infinitely many periodic solutions still exist in this case. These solutions have periods which are large integer multiples of the period of the forcing, and rotate exactly once around the origin in their period time.

Relative Periodic Orbits of Symmetric Lagrangian Systems

stability and attraction domains of traffic equilibria in day-to-day dynamical system formulation

در این پژوهش مسئله واگذاری ترافیک را از دید سیستم های دینامیکی فرمول بندی می کنیم.فرض کرده ایم که همه فاکتورهای وابسته در طول زمان ثابت باشند و تعادل کاربر را از طریق فرایند منظم روزبه روز پیگیری کنیم.دینامیک ترافیک توسط یک نگاشت بازگشتی نشان داده می شود که تکامل سیستم در طول زمان را نشان می دهد.پایداری تعادل و دامنه جذب را توسط مطالعه ویژگی های توپولوژیکی تکامل سیستم تجزیه و تحلیل می کنیم.پاید...

Numerical Continuation of Symmetric Periodic Orbits

The bifurcation theory and numerics of periodic orbits of general dynamical systems is well developed, and in recent years there has been rapid progress in the development of a bifurcation theory for symmetric dynamical systems. But there are hardly any results on the numerical computation of those bifurcations yet. In this paper we show how spatiotemporal symmetries of periodic orbits can be e...

Three classes of newtonian three-body planar periodic orbits.

We present the results of a numerical search for periodic orbits of three equal masses moving in a plane under the influence of Newtonian gravity, with zero angular momentum. A topological method is used to classify periodic three-body orbits into families, which fall into four classes, with all three previously known families belonging to one class. The classes are defined by the orbits' geome...