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1.
具有渐近平均跟踪性质的系统   总被引:1,自引:0,他引:1  
简记渐近平均跟踪性质为AASP.对于紧致度量空间上的连续映射f,证明了:(1)f有AASP当且仅当其逆极限空间上的移位映射有AASP;(2)若f有AASP且是等度连续的,则f是极小同胚.此外,讨论了AASP的拓扑共轭不变性.  相似文献   

2.
In J. Math. Anal. Appl. 189 (1995) 409-423, Corless and Pilyugin proved that weak shadowing is a C0 generic property in the space of discrete dynamical systems on a compact smooth manifold M. In our paper we give another proof of this theorem which does not assume that M has a differential structure. Moreover, our method also works for systems on some compact metric spaces that are not manifolds, such as a Hilbert cube (or generally, a countably infinite Cartesian product of manifolds with boundary) and a Cantor set.  相似文献   

3.
This is a survey of the main results obtained in the theory of pseudo-orbit shadowing in dynamical systems in the first decade of the 21st century. The main directions are shadowing and structural stability, C 1-interiors of sets of systems with the shadowing property, shadowing properties equivalent to the structural stability, and the denseness problem.  相似文献   

4.
Let X be a divergence-free vector field on a three-dimensional compact connected Riemannian manifold. In this paper, we show that if X is in the C1-interior of the set of divergence-free vector fields which satisfy the average shadowing property then X is Anosov. We also obtain similar result for asymptotic average shadowing property.  相似文献   

5.
Let M be a closed smooth manifold M, and let f : M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set Λ of f . We show that if f has the C1-stably average shadowing property on Λ, then Λ admits a dominated splitting.  相似文献   

6.
Let X be a compact metric space and f: X → X be a continuous map. In this paper, we investigate the relationships between the asymptotic average shadowing property (Abbrev. AASP) and other notions known from topological dynamics. We prove that if f has the AASP and the minimal points of f are dense in X, then for any n ? 1, f × f × ? × f(n times) is totally strongly ergodic. As a corollary, it is shown that if f is surjective and equicontinuous, then f does not have the AASP. Moreover we prove that if f is point distal, then f does not have the AASP. For f: [0, 1] → [0, 1] being surjective continuous, it is obtained that if f has two periodic points and the AASP, then f is Li-Yorke chaotic.  相似文献   

7.
In this paper we consider generalized dynamical systems whose integral vortex (that is, the set of all trajectories of the system starting at a given point) is an acyclic set in the corresponding space of curves. For such systems we apply the theory of fixed points for multi-valued maps in order to prove the existence of rest points. In this way we obtain new existence theorems for rest points of generalized dynamical systems. Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 28–36, January, 1999.  相似文献   

8.
We report the discovery of an infinite quantity of Mandelbrot-like sets in the real parameter space of the Hénon map, a bidimensional diffeomorphism not obeying the Cauchy–Riemann conditions and having no critical points. For practical applications, this result shows to be possible to stabilize infinitely many complex phases by tuning real parameters only. To cite this article: A. Endler, J.A.C. Gallas, C. R. Acad. Sci. Paris, Ser. I 342 (2006).  相似文献   

9.
Given a rational map :11 defined over a number field K, we provea finiteness result for -preperiodic points which are S-integralwith respect to a non-preperiodic point P, provided that P satisfiesa certain local condition at each place. This verifies a specialcase of a conjecture of Ih.  相似文献   

10.
Critical points with lack of compactness and singular dynamical systems   总被引:1,自引:0,他引:1  
Sunto Si prova l'esistenza di punti critici di funzionali che non verificano la condizione (PS).I teoremi astratti vengono applicati per trovare soluzioni periodiche di sistemi dinamici con potenziali sia limitati sia con singolarità.

This work has been done during a visit at the Math. Dept. of the University of Chicago. The Authors whish to thank for the kind hospitality.

Supported by Ministero Pubblica Istruzione, 40%, Gruppo Nazionale «Calcolo delle Variazioni».  相似文献   

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Given a free ultrafilter p on ? we say that x ∈ [0, 1] is the p-limit point of a sequence (x n ) n∈? ? [0, 1] (in symbols, x = p -lim n∈? x n ) if for every neighbourhood V of x, {n ∈ ?: x n V} ∈ p. For a function f: [0, 1] → [0, 1] the function f p : [0, 1] → [0, 1] is defined by f p (x) = p -lim n∈? f n (x) for each x ∈ [0, 1]. This map is rarely continuous. In this note we study properties which are equivalent to the continuity of f p . For a filter F we also define the ω F -limit set of f at x. We consider a question about continuity of the multivalued map xω f F (x). We point out some connections between the Baire class of f p and tame dynamical systems, and give some open problems.  相似文献   

15.
Let f be a continuous map of a compact metric space. Assuming shadowing for f we relate the average shadowing property of f to transitivity and its variants. Our results extend and complete the work of Sakai [K. Sakai, Various shadowing properties for positively expansive maps, Topology Appl. 131 (2003) 15-31].  相似文献   

16.
We prove that if for a continuous map ff on a compact metric space XX, the chain recurrent set, R(f)R(f) has more than one chain component, then ff does not satisfy the asymptotic average shadowing property. We also show that if a continuous map ff on a compact metric space XX has the asymptotic average shadowing property and if AA is an attractor for ff, then AA is the single attractor for ff and we have A=R(f)A=R(f). We also study diffeomorphisms with asymptotic average shadowing property and prove that if MM is a compact manifold which is not finite with dimM=2dimM=2, then the C1C1 interior of the set of all C1C1 diffeomorphisms with the asymptotic average shadowing property is characterized by the set of ΩΩ-stable diffeomorphisms.  相似文献   

17.
The aim of this paper is to relate the almost average shadowing property (ALASP) with various variants of ergodicity and with some other dynamical properties. We also study the relation of the ALASP with proximality.  相似文献   

18.
Let k be a number field with algebraic closure , and let S be a finite set of primes of k, containing all the infinite ones. Consider a Chebyshev dynamical system on P2. Fix the effective divisor D of P2 that is equal to a line nondegenerate on2[−2,2]. Then we will prove that the set of preperiodic points on which are S-integral relative to D is not Zariski dense in P2.  相似文献   

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In this paper, the notion of the Lipschitz inverse shadowing property with respect to two classes of d-methods that generate pseudotrajectories of dynamical systems is introduced. It is shown that if a diffeomorphism of a Euclidean space has the Lipschitz inverse shadowing property on the trajectory of an individual point, then the Mañé analytic strong transversality condition must be satisfied at this point. This result is used in the proof of the main theorem: a diffeomorphism of a smooth closed manifold that has the Lipschitz inverse shadowing property is structurally stable.  相似文献   

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