ترغب بنشر مسار تعليمي؟ اضغط هنا

Families of piecewise linear maps with constant Lyapunov exponent

405   0   0.0 ( 0 )
 نشر من قبل Vicente Botella-Soler
 تاريخ النشر 2012
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant. We provide numerical evidence of this fact and we prove it analytically for some special cases. The mechanism is very different from that of the logistic map and we conjecture that the Lyapunov plateaus reflect arithmetic relations between the slopes.



قيم البحث

اقرأ أيضاً

259 - Xin-Chu Fu , Peter Ashwin 2003
In this paper a class of linear maps on the 2-torus and some planar piecewise isometries are discussed. For these discontinuous maps, by introducing codings underlying the map operations, symbolic descriptions of the dynamics and admissibility condit ions for itineraries are given, and explicit expressions in terms of the codings for periodic points are presented.
We investigate the parametric evolution of riddled basins related to synchronization of chaos in two coupled piecewise-linear Lorenz maps. Riddling means that the basin of the synchronized attractor is shown to be riddled with holes belonging to anot her basin in an arbitrarily fine scale, which has serious consequences on the predictability of the final state for such a coupled system. We found that there are wide parameter intervals for which two piecewise-linear Lorenz maps exhibit riddled basins (globally or locally), which indicates that there are riddled basins in coupled Lorenz equations, as previously suggested by numerical experiments. The use of piecewise-linear maps makes it possible to prove rigorously the mathematical requirements for the existence of riddled basins.
124 - Yian Ma , Ruoshi Yuan , Yang Li 2013
This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means. Special a ttention is stressed upon a problem not formerly solved: to impose consistent boundary conditions on the Lyapunov function in each linear region. By successfully solving the problem, the authors construct continuous Lyapunov functions in the whole state space. It is further demonstrated that the Lyapunov functions constructed explain for the different bifurcations leading to the emergence of limit cycle oscillation.
We show that enhanced wavefunction localization due to the presence of short unstable orbits and strong scarring can rely on completely different mechanisms. Specifically we find that in quantum networks the shortest and most stable orbits do not sup port visible scars, although they are responsible for enhanced localization in the majority of the eigenstates. Scarring orbits are selected by a criterion which does not involve the classical Lyapunov exponent. We obtain predictions for the energies of visible scars and the distributions of scarring strengths and inverse participation ratios.
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic invariant set is heterogeneous when arbitrarily close to each point of the set there are different periodic points with different numbers of unstable dimensions. We call such dynamics heterogeneous chaos (or hetero-chaos), While we believe it is common for physical systems to be hetero-chaotic, few explicit examples have been proved to be hetero-chaotic. Here we present two more explicit dynamical systems that are particularly simple and tractable with computer. It will give more intuition as to how complex even simple systems can be. Our maps have one dense set of periodic points whose orbits are 1D unstable and another dense set of periodic points whose orbits are 2D unstable. Moreover, they are ergodic relative to the Lebesgue measure.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا