In this paper, we discussed the cofinite sensitivity, shadowing property (SP), P-chaos, and chain mixing of a system induced by symmetric maps (Cournot maps) D(a,b)=(t(b),s(a)) over product space G×H, where s:G→H, t:H→G, a∈G, b∈H, G H are closed subintervals with G,H⊂R. The following hold: (1) D is cofinitely sensitive equivalent to D2|Γ1 or D2|Γ2 being sensitive, Γ1={(t(b),b):b∈H}, Γ2={(a,s(a)):a∈G}. (2) possessing an SP both s∘t t∘s having SP. (3) possesses if only does as well. (4)...

This paper is concerned with some stronger forms of sensitivity for measure-preserving maps and semiflows on probability spaces. A new form introduced, called ergodic sensitivity. It shown that, a metric space fully supported measure, if map weak mixing, then it ergodically sensitive multisensitive; strong cofinitely sensitive, where not required that the continuous compact. Similar results are obtained, in result about compact sense semiflow continuous. In addition, relationships between...

We prove that if a continuous, Lyapunov stable map f from compact metric space X into itself is topologically transitive and has the asymptotic average shadowing property, then consisting of one point. As an application, we identity i : → does not have where with at least two points.

Let [Formula: see text] be a continuous selfmap of nontrivial compact metric space text]. This paper derives the large deviations theorem in sequence. It is shown that if satisfies sequence then it an E-system which implies syndetically transitive, and pair infinite space, sensitive, ergodically sensitive. Moreover, proved syndetic sequence, ergodic measure with supp[Formula: Our main results extend improve corresponding literature.

In this paper, it is proved that the product system (X × Y, T S) multi-F -sensitive (resp., (F 1 , F 2 )sensitive) if and only (X, ) or (Y, )-sensitive) when Furstehberg families have Ramsey property, improving main results in [N.Deǧirmenci, S ¸.

Let (f n ) be a given sequence of continuous selfmaps compact metric space X which converges uniformly to selfmap f X, and let F, F 1 , 2 Furstenberg families.In this paper, we obtain an equivalence condition for the uniform limit map F-transitive or weakly F-sensitive (F )-sensitive necessary )-sensitive.Our results extend improve some existing ones.

Let (X, d) be a compact nontrivial metric space and H(X) the set of all homeomorphisms X. A system f∈H(X) is said to chaotic if some positive iteration f semiconjugated shift map σ:Σ→Σ. For any k≠0 f∈H(X), we show that only fk chaotic. Furthermore, present sufficient conditions for In particular, it shown (1) If in sense Devaney has shadowing property, then chaotic; (2) g∈H(X′) have f×g or g chaotic, where X′ space; (3) continuum X P-chaotic, As an application, characterize entropy f∈H(T)...

In this paper, we are concerned solely with the ergodic sensitivity for maps (resp. semi-flows), where these and semi-flows may not be continuous (in topology). A few new sufficient conditions under which a map semi-flow) on metric space is ergodically sensitive presented, such particular, prove that topologically strong ergodicity of measure-preserving probability fully supported measure implies its ergodical sensitivity.

In this paper, let (X, f 1,∞ ) be a non-autonomous discrete system on compact metric space X.For positive k, the properties P (k) and Q(k) of Furstenberg families are introduced for any integer k > 0. Based two properties, we prove that (F 1 , F 2 )-sensitivity weak inherited under iterations.

In this paper, the concepts of F-collective sensitivity (resp.(F 1 , F 2 )-collective sensitivity) and compact-type (resp.compact-type (F are introduced as stronger forms traditional for dynamical systems Hausdorff locally compact second countable (HLCSC) systems, respectively, where F, Furstenberg families.It is proved that F-sensitivity )-sensitivity) induced hyperspace system defined on space non-empty subsets or finite (Vietoris topology) equivalent to original system; all nonempty...

Let (E,h1,∞) be a nonautonomous discrete dynamical system (briefly, N.D.D.S.) that is defined by sequence (hj)j=1∞ of continuous maps hj:E→E over nontrivial metric space (E,d). This paper defines and discusses some forms ergodicity sensitivity for the upper density, lower positive integers. Under conditions, if rate convergence at which converges to limit map h “fast enough” with respect integers density one, it shown several properties N.D.D.S. are same as those (E,h). Some sufficient...