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1.
A definition of hyperbolicity for dynamical systems generated by set-valued mappings of general form in terms of local selectors
is given. It is shown that a system hyperbolic in this sense has the shadowing and inverse shadowing properties. It is also
shown that the hyperbolicity property holds true for a certain class of set-valued mappings where images of points are convex
polytopes. Bibliography: 13 titles. 相似文献
2.
S. Y. Pilyugin 《Journal of Difference Equations and Applications》2013,19(3-4):271-282
We describe several generalizations of the classical notion of hyperbolicity for a sequence of linear mappings. It is shown that the following three statements are equivalent: (i) the corresponding linear non-homogeneous system has a bounded solution for any bounded nonhomogeneity, (ii) the sequence has a (C, λ)-structure, (iii) the sequence is piecewise hyperbolic with long enough intervals of hyperbolicity. 相似文献
3.
A class of biholomorphic mappings named “quasi-convex mapping” is introduced in the unit ball of a complex Banach space. It
is proved that this class of mappings is a proper subset of the class of starlike mappings and contains the class of convex
mappings properly, and it has the same growth and covering theorems as the convex mappings. Furthermore, when the Banach space
is confined to ℂn, the “quasi-convex mapping” is exactly the “quasi-convex mapping of type A” introduced by K. A. Roper and T. J. Suffridge. 相似文献
4.
Gromov Hyperbolicity of Riemann Surfaces 总被引:1,自引:0,他引:1
Jos M. RODPIGUEZ Eva TOURIS 《数学学报(英文版)》2007,23(2):209-228
We study the hyperbolicity in the Gromov sense of Riemann surfaces. We deduce the hyperbolicity of a surface from the hyperbolicity of its "building block components". We also prove the equivalence between the hyperbolicity of a Riemann surface and the hyperbolicity of some graph associated with it. These results clarify how the decomposition of a Riemann surface into Y-pieces and funnels affects the hyperbolicity of the surface. The results simplify the topology of the surface and allow us to obtain global results from local information. 相似文献
5.
N. B. Zhuravlev 《Journal of Mathematical Sciences》2008,153(5):683-709
In this paper, a hyperbolicity criterion for periodic solutions of nonlinear functional-differential equations is constructed
in terms of zeros of the characteristic function. In the earlier papers in this area, necessary and sufficient conditions
were different from each other. Moreover, it was assumed that if the period of the investigated solution is irrational, then
that solution admits a rational approximation. In this paper, we obtain necessary and sufficient conditions of the hyperbolicity.
It is proved (and the proof is constructive) that a rational approximation exists for any irrational period. All the results
are obtained for the case of several rational delays.
__________
Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 21, Proceedings of the Seminar on Differential and Functional Differential Equations Supervised by A. Skubachevskii (Peoples’
Friendship University of Russia), 2007. 相似文献
6.
7.
《Set-Valued Analysis》2008,16(2-3):199-227
The paper contains two groups of results. The first are criteria for calmness/subregularity for set-valued mappings between
finite-dimensional spaces. We give a new sufficient condition whose subregularity part has the same form as the coderivative
criterion for “full” metric regularity but involves a different type of coderivative which is introduced in the paper. We
also show that the condition is necessary for mappings with convex graphs. The second group of results deals with the basic
calculus rules of nonsmooth subdifferential calculus. For each of the rules we state two qualification conditions: one in
terms of calmness/subregularity of certain set-valued mappings and the other as a metric estimate (not necessarily directly
associated with aforementioned calmness/subregularity property). The conditions are shown to be weaker than the standard Mordukhovich–Rockafellar
subdifferential qualification condition; in particular they cover the cases of convex polyhedral set-valued mappings and,
more generally, mappings with semi-linear graphs. Relative strength of the conditions is thoroughly analyzed. We also show,
for each of the calculus rules, that the standard qualification conditions are equivalent to “full” metric regularity of precisely
the same mappings that are involved in the subregularity version of our calmness/subregularity condition.
The research of Jiří V. Outrata was supported by the grant A 107 5402 of the Grant Agency of the Academy of Sciences of the
Czech Republic. 相似文献
8.
In this paper we extend the coupled contraction mapping theorem proved in partially ordered metric spaces by Gnana Bhaskar
and Lakshmikantham (Nonlinear Anal. TMA 65:1379–1393, 2006) to a coupled coincidence point result for a pair of compatible mappings. A control function has been used in our theorem.
The mappings are assumed to satisfy a weak contractive inequality. Our theorem improves the results of Harjani et al. (Nonlinear
Anal. TMA 74:1749–1760, 2011). The result we have established is illustrated with an example which also shows that the improvement is actual. 相似文献
9.
It is shown that mappings in ℝn with finite distortion of area in all dimensions 1 ≤ k ≤ n − 1 satisfy certain modulus inequalities in terms of inner and outer dilatations of the mappings; in particular, generalizations
of the well-known Poletskii inequality for quasiregular mappings are proved. The theory developed is applicable, for example,
to the class of finitely bi-Lipschitz mappings, which is a natural generalization of the bi-Lipschitz mappings, as well as
isometries and quasi-isometries in ℝn. 相似文献
10.
In this paper, a class of biholomorphic mappings called complete quasiconvex mappings is introduced and studied in bounded
convex Reinhardt domains of ℂ
n
. Through a detailed analysis of the analytic characterization for this class of mappings, it is shown that this class of
mappings contains the convex mappings and is also a subset of the class of starlike mappings. In the special case of the polydisc,
a decomposition theorem is established for the complete quasiconvex mappings, which in turn is used to derive an improved
sufficient condition for the convex mappings.
Translated from Chinese Annals of Mathematics (Series A) 相似文献
11.
V. A. Dobrynskii 《Mathematical Notes》1995,58(5):1147-1155
A lower estimate for the number of different invariant subsets of the set of nonwandering points for a class of unimodal mappings
is given. Sufficient conditions for such a mapping to have periodic points of arbitrarily large period are described. The
machinery of the appearance of such points may be of very different nature. The existence of mappings with trajectory behavior
chaotic in the Li-York sense is established. Conditions for the domain of these trajectories to be arbitrary small are given.
Therefore, such trajectories cannot be found by numerical methods.
Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 669–680, November, 1995. 相似文献
12.
In this article we study the hyperbolicity in the Gromov sense of metric spaces. We deduce the hyperbolicity of a space from
the hyperbolicity of its “building block components,” which can be joined following an arbitrary scheme. These results are
especially valuable since they simplify notably the topology and allow to obtain global results from local information. Some
interesting theorems about the role of punctures and funnels on the hyperbolicity of Riemann surfaces can be deduced from
the conclusions of this article. 相似文献
13.
Peter H?st? Ana Portilla Jos�� M. Rodr��guez Eva Tour��s 《Mediterranean Journal of Mathematics》2011,8(1):49-67
In this article we prove comparative results on the Gromov hyperbolicity of plane domains equipped with the quasihyperbolic
metric. By a comparative result we mean one which assumes hyperbolicity in one domain and obtains it in a different domain
somehow related to the original one. We derive a characterization (simple to check in practical cases) of the Gromov hyperbolicity
of a plane domain Ω* obtained by deleting from the original domain Ω any uniformly separated union of compact sets. We present
as well a result about stability of hyperbolicity. 相似文献
14.
Baouendi M. S. Mir Nordine Rothschild Linda Preiss 《Journal of Geometric Analysis》2002,12(4):543-580
Results on finite determination and convergence of formal mappings between smooth generic submanifolds in ℂ
N
are established in this article. The finite determination result gibes sufficient conditions to guarantee that a formal map
is uniquely determined by its jet, of a preassigned order, at a point. Convergence of formal mappings for real-analytic generic
submanifolds under appropriate assumptions is proved, and natural geometric conditions are given to assure that if two germs
of such submanifolds are formally equivalent, then, they are necessarily biholomorphically equivalent. It is also shown that
if two real-algebraic hypersurfaces in ℂ
N
are biholomorphically equivalent, then, they are algebraically equivalent. All the results are first proved in the more general
context of “reflection ideals” associated to formal mappings between formal as well as real-analytic and real-algebraic manifolds. 相似文献
15.
In this paper, a class of biholomorphic mappings named quasi-convex mapping of order α in the unit ball of a complex Banach space is introduced. When the Banach space is confined to ℂ
n
, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems
of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order
α defined on the polydisc in ℂ
n
and on the unit ball in a complex Banach space, respectively.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
16.
Bao She Wei 《数学学报(英文版)》2002,18(4):701-718
In this paper, we consider certain mappings, ${\mathcal {M}}In this paper, we consider certain mappings, ℳ , sufficiently close to an integrable one, which is weakly reversible with
respct to the mappings ? sufficiently close to an involution of tye (m, n), where m, n∈Z
+ are arbitrary. Under some weak non-degeneracy condition, we construct a uniform KAM iteration for providing the existence
of a Cantor family of m-tori invariant under the reversible mappings ℳ and the reversing mapping ?.
Received September 29, 1999, Accepted July 18, 2000 相似文献
17.
18.
Pietsch’s domination theorem, which is known for linear, multilinear and polynomial mappings, is extended to a larger class
of nonlinear mappings. 相似文献
19.
We discuss two notions of hyperbolicity for finite–time linear differential equations. The first notion (D–hyperbolicity) is based on the dynamic (or EPH) partition, the second (M–hyperbolicity) is motivated by exponential dichotomies. We study conditions under which D–hyperbolicity implies M–hyperbolicity. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
The complementarity problem is one of the basic topics in nonlinear analysis; however, the methods for solving complementarity
problems are usually developed for problems with single-valued mappings. In this paper we examine a class of complementarity
problems with multi-valued mappings and propose an extension of the Gauss–Seidel algorithm for finding its solution. Its convergence
is proved under off-diagonal antitonicity assumptions. Applications to Walrasian type equilibrium problems and to nonlinear
input–output problems are also given.
In this work, the authors were supported by Brescia University grant PRIN - 2006: “Oligopolistic models and order monotonicity
properties”, the third author was also supported by the joint RFBR–NNSF grant, project No. 07-01-92101. 相似文献