ترغب بنشر مسار تعليمي؟ اضغط هنا

Random Delta-Hausdorff-attractors

85   0   0.0 ( 0 )
 نشر من قبل Maite Isabel Wilke Berenguer
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Global random attractors and random point attractors for random dynamical systems have been studied for several decades. Here we introduce two intermediate concepts: $Delta$-attractors are characterized by attracting all deterministic compact sets of Hausdorff dimension at most $Delta$, where $Delta$ is a non-negative number, while cc-attractors attract all countable compact sets. We provide two examples showing that a given random dynamical system may have various different $Delta$-attractors for different values of $Delta$. It seems that both concepts are new even in the context of deterministic dynamical systems.



قيم البحث

اقرأ أيضاً

125 - Zhenxin Liu 2007
In the first part of this paper, we generalize the results of the author cite{Liu,Liu2} from the random flow case to the random semiflow case, i.e. we obtain Conley decomposition theorem for infinite dimensional random dynamical systems. In the secon d part, by introducing the backward orbit for random semiflow, we are able to decompose invariant random compact set (e.g. global random attractor) into random Morse sets and connecting orbits between them, which generalizes the Morse decomposition of invariant sets originated from Conley cite{Con} to the random semiflow setting and gives the positive answer to an open problem put forward by Caraballo and Langa cite{CL}.
244 - Bixiang Wang 2014
In this paper, we introduce concepts of pathwise random almost periodic and almost automorphic solutions for dynamical systems generated by non-autonomous stochastic equations. These solutions are pathwise stochastic analogues of deterministic dynami cal systems. The existence and bifurcation of random periodic (random almost periodic, random almost automorphic) solutions have been established for a one-dimensional stochastic equation with multiplicative noise.
78 - Zhenxin Liu 2006
Conley index theory is a very powerful tool in the study of dynamical systems, differential equations and bifurcation theory. In this paper, we make an attempt to generalize the Conley index to discrete random dynamical systems. And we mainly follow the Conley index for maps given by Franks and Richeson in [6]. Furthermore, we simply discuss the relations of isolated invariant sets between time-continuous random dynamical systems and the corresponding time-$h$ maps. For applications we give several examples to illustrate our results.
179 - U. Haboeck 2008
We show that the twisted planar random walk - which results by summing up stationary increments rotated by multiples of a fixed angle - is recurrent under diverse assumptions on the increment process. For example, if the increment process is alpha-mi xing and of finite second moment, then the twisted random walk is recurrent for every angle fixed choice of the angle out of a set of full Lebesgue measure, no matter how slow the mixing coefficients decay.
68 - Erik Lundberg 2020
We study the number and distribution of the limit cycles of a planar vector field whose component functions are random polynomials. We prove a lower bound on the average number of limit cycles when the random polynomials are sampled from the Kostlan- Shub-Smale ensemble. For the related Bargmann-Fock ensemble of real analytic functions we establish an asymptotic result for the average number of empty limit cycles (limit cycles that do not surround other limit cycles) in a large viewing window. Concerning the special setting of limit cycles near a randomly perturbed center focus (where the perturbation has i.i.d. coefficients) we prove that the number of limit cycles situated within a disk of radius less than unity converges almost surely to the number of real zeros of a certain random power series. We also consider infinitesimal perturbations where we obtain precise asymptotics on the global count of limit cycles for a family of models. The proofs of these results use novel combinations of techniques from dynamical systems and random analytic functions.
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