A ug 2 00 9 CAN CLASSICAL LINEAR HARMONIC OSCILLATOR HOLD CHAOTIC ( FRACTAL ) DYNAMICS
نویسنده
چکیده
In this work a classical linear harmonic oscillator, evolving during a small time interval (so that simple non-linear, second order Taylor approximation of the dynamics is satisfied) and restarting (by a mechanism) in a strictly chosen series of the time moments, is considered. It is shown that given linear oscillator behaves dynamically analogously to discrete logistic equation, which, as an especial case, includes chaotic (fractal) behaviour too. (All this refers too on the analogous quantum systems, e.g. ammonia molecule with simple vibration dynamics of the atoms many times perturbed by measurements in strictly defined time moments.)
منابع مشابه
IC/99/188 United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS HARMONIC OSCILLATIONS, CHAOS AND SYNCHRONIZATION IN SYSTEMS CONSISTING OF VAN DER POL OSCILLATOR COUPLED TO A LINEAR OSCILLATOR
This paper deals with the dynamics of a model describing systems eonsisting of the classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. Both the forced and autonomous cases are considered. Harmonic response is investigated along with its stability boundaries. Condition for quenching phenomena in the autonomous case is derived. Neimark bifurcation is observed and it is...
متن کاملar X iv : m at h / 05 05 46 8 v 2 [ m at h . A P ] 2 2 A ug 2 00 5 INSTABILITY FOR SEMI - CLASSICAL SCHRÖDINGER EQUATIONS
Using WKB methods for very small times, we prove some instability phenomena for semi-classical (linear or) nonlinear Schrödinger equations. The main step of the analysis consists in reducing the problem to an ordinary differential equation. The solution to this o.d.e. is explicit, and the instability mechanism is due to the presence of the semi-classical parameter. For nonlin-ear equations, our...
متن کاملAlgorithm for the Determination of the Resonances of Anharmonic Damped Oscillators
In addition to the passive observation of a non linear oscillator and the description of the measured data with Lyapounow exponents [1, 2], fractal dimensions [3-5], entropies [6], etc. it is possible to charcterize a non-linear oscillator by an active method, namely by determining its response to specific perturbations. The resonances of harmonic systems which are brought about by a sinusoida...
متن کاملDissipative dynamics in a finite chaotic environment: Relationship between damping rate and Lyapunov exponent.
We consider the energy flow between a classical one-dimensional harmonic oscillator and a set of N two-dimensional chaotic oscillators, which represents the finite environment. Using linear response theory we obtain an analytical effective equation for the system harmonic oscillator, which includes a frequency dependent dissipation, a shift, and memory effects. The damping rate is expressed in ...
متن کاملChaos in the Quantum Double Well Oscillator: The Ehrenfest View Revisited
We treat the double well quantum oscillator from the standpoint of the Ehrenfest equation but in a manner different from Pattanayak and Schieve. We show that for short times there can be chaotic motion due to quantum fluctuations, but over sufficiently long times the behaviour is normal. It is generally agreed that the full quantum dynamics does not exhibit chaos. For systems which exhibit chao...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009