ترغب بنشر مسار تعليمي؟ اضغط هنا

On Katznelsons Question for skew product systems

110   0   0.0 ( 0 )
 نشر من قبل Daniel Glasscock
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Katznelsons Question is a long-standing open question concerning recurrence in topological dynamics with strong historical and mathematical ties to open problems in combinatorics and harmonic analysis. In this article, we give a positive answer to Katznelsons Question for certain towers of skew product extensions of equicontinuous systems, including systems of the form $(x,t) mapsto (x + alpha, t + h(x))$. We describe which frequencies must be controlled for in order to ensure recurrence in such systems, and we derive combinatorial corollaries concerning the difference sets of syndetic subsets of the natural numbers.



قيم البحث

اقرأ أيضاً

The first part of the paper is devoted to studying the continuous dependence of the solutions of Caratheodory constant delay differential equations where the vector fields satisfy classical cooperative conditions. As a consequence, when the set of co nsidered vector fields is invariant with respect to the time-translation map, the continuity of the respective induced skew-product semiflows is obtained. These results are important for the study of the long-term behavior of the trajectories. In particular, the construction of semicontinuous semiequilibria and equilibria is extended to the context of ordinary and delay Caratheodory differential equations. Under appropriate assumptions of sublinearity, the existence of a unique continuous equilibrium, whose graph coincides with the pullback attractor for the evolution processes, is shown. The conditions under which such a solution is the forward attractor of the considered problem are outlined. Two examples of application of the developed tools are also provided.
Starting from a discrete $C^*$-dynamical system $(mathfrak{A}, theta, omega_o)$, we define and study most of the main ergodic properties of the crossed product $C^*$-dynamical system $(mathfrak{A}rtimes_alphamathbb{Z}, Phi_{theta, u},om_ocirc E)$, $E :mathfrak{A}rtimes_alphamathbb{Z}rightarrowga$ being the canonical conditional expectation of $mathfrak{A}rtimes_alphamathbb{Z}$ onto $mathfrak{A}$, provided $ainaut(ga)$ commute with the $*$-automorphism $th$ up tu a unitary $uinga$. Here, $Phi_{theta, u}inaut(mathfrak{A}rtimes_alphamathbb{Z})$ can be considered as the fully noncommutative generalisation of the celebrated skew-product defined by H. Anzai for the product of two tori in the classical case.
148 - Kaijen Cheng 2017
In this paper we give an elementary treatment of the dynamics of skew tent maps. We divide the two-parameter space into six regions. Two of these regions are further subdivided into infinitely many regions. All of the regions are given explicitly. We find the attractor in each subregion, determine whether the attractor is a periodic orbit or is chaotic, and also determine the asymptotic fate of every point. We find that when the attractor is chaotic, it is either a single interval or the disjoint union of a finite number of intervals; when it is a periodic orbit, all periods are possible. Sometimes, besides the attractor, there exists an invariant chaotic Cantor set.
122 - Matthieu Astorg 2020
We continue our investigation of the parameter space of families of polynomial skew products. Assuming that the base polynomial has a Julia set not totally disconnected and is neither a Chebyshev nor a power map, we prove that, near any bifurcation p arameter, one can find parameters where $k$ critical points bifurcate emph{independently}, with $k$ up to the dimension of the parameter space. This is a striking difference with respect to the one-dimensional case. The proof is based on a variant of the inclination lemma, applied to the postcritical set at a Misiurewicz parameter. By means of an analytical criterion for the non-vanishing of the self-intersections of the bifurcation current, we deduce the equality of the supports of the bifurcation current and the bifurcation measure for such families. Combined with results by Dujardin and Taflin, this also implies that the support of the bifurcation measure in these families has non-empty interior.As part of our proof we construct, in these families, subfamilies of codimension 1 where the bifurcation locus has non empty interior. This provides a new independent proof of the existence of holomorphic families of arbitrarily large dimension whose bifurcation locus has non empty interior. Finally, it shows that the Hausdorff dimension of the support of the bifurcation measure is maximal at any point of its support.
In this paper we discuss the question of how to decide when a general chemical reaction system is incapable of admitting multiple equilibria, regardless of parameter values such as reaction rate constants, and regardless of the type of chemical kinet ics, such as mass-action kinetics, Michaelis-Menten kinetics, etc. Our results relate previously described linear algebraic and graph-theoretic conditions for injectivity of chemical reaction systems. After developing a translation between the two formalisms, we show that a graph-theoretic test developed earlier in the context of systems with mass action kinetics, can be applied to reaction systems with arbitrary kinetics. The test, which is easy to implement algorithmically, and can often be decided without the need for any computation, rules out the possibility of multiple equilibria for the systems in question.
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