It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cy...It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cylinder.By constructing a bounded solution of the monotone recurrence relation,the main conclusion in this paper is acquired:The induced homeomorphism has Birkhoff orbits provided there is a compact forward-invariant set.Therefore,it generalizes Angenent's results in low-dimensional cases.展开更多
This paper provides a regularity theorem for certain 2nth-order differential operator Bλthat arises in considering some moving behaviors of certain objects, which includes (n + 2)homeomorphisms and extended homeomorp...This paper provides a regularity theorem for certain 2nth-order differential operator Bλthat arises in considering some moving behaviors of certain objects, which includes (n + 2)homeomorphisms and extended homeomorphisms in 'real nonlinear case' or (n + 3) linearhomeomorphisms and extened linear homeomorphisms in 'complex linear case' for this operator. It is useful to illustrate some stabilities in both directions of certain objects in theirmoving processes.展开更多
In this paper we give a new and elementary proof to the following fact:each closed orientable surface of positive genus admits a both chaotic and expansive homeomorphism.Further more,we show that the homeomorphisms gi...In this paper we give a new and elementary proof to the following fact:each closed orientable surface of positive genus admits a both chaotic and expansive homeomorphism.Further more,we show that the homeomorphisms given are also weakly mixing.展开更多
Let QS* (S 1) be the space of quasisymmetric homeomorphisms of the unit circle such that the corresponding subspace of the universal Teichmu¨ller space has Weil-Petersson metric.In this paper we give a necessary ...Let QS* (S 1) be the space of quasisymmetric homeomorphisms of the unit circle such that the corresponding subspace of the universal Teichmu¨ller space has Weil-Petersson metric.In this paper we give a necessary condition for a quasisymmetric homeomorphism to belong to QS *(S 1) from the aspect of cross-ratio distortion.展开更多
Let f ： Ω→ f（Ω） belong to R^n be a W^1,1-homeomorphism with L^1-inegrable inner We show that finiteness of min{lipf（x）, kf（x））, for every x∈ Ω／E, implies that f^-1 ∈ W^1,n and has finite distortion, pro...Let f ： Ω→ f（Ω） belong to R^n be a W^1,1-homeomorphism with L^1-inegrable inner We show that finiteness of min{lipf（x）, kf（x））, for every x∈ Ω／E, implies that f^-1 ∈ W^1,n and has finite distortion, provided that the exceptional set E has σ-finite H^1-measure.Moreover, f has finite distortion, differentiable a.e. and the Jacobian Jf 〉 0 a.e.展开更多
Suppose that D is a domain in (n 2) and y= f(x): D → R^n is a homeomorphism. We prove that if the modulus dilatation K(x, f) satisfies the condition A then f(x) is ACL.
Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold BM, and fπ ： π1 （M）→π1 （M） be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the...Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold BM, and fπ ： π1 （M）→π1 （M） be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the rank of the fixed subgroup of fπ, namely, rankFix（fπ） 〈 2rankπ1（M）, which is an analogue of inequalities on surface groups and hyperbolic 3-manifold groups.展开更多
We introduce the concept of asymptotic pseudo orbit tracing property (APOTP) and obtain a new condition by the APOTP for which a homeomor-phism is a non-wandering homeomorphism.
Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m ...Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r＋1/rα^r（α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.展开更多
Let X be a Jordan domain satisfying certain hyperbolic growth conditions.Assume that φ is a homeomorphism from the boundary ?X of X onto the unit circle.Denote by h the harmonic diffeomorphic extension of φ from X o...Let X be a Jordan domain satisfying certain hyperbolic growth conditions.Assume that φ is a homeomorphism from the boundary ?X of X onto the unit circle.Denote by h the harmonic diffeomorphic extension of φ from X onto the unit disk.We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of h.These generalize the Sobolev regularity of h in [A.Koski,J.Onninen,Sobolev homeomorphic extensions,J.Eur.Math.Soc.23(2021) 4065-4089,Theorem 3.1].展开更多
In this paper,we consider the following systems x″+ Bx′+ gradG(x,t) = 0.Weak sufficient condition for the existence of a unique 2π-periodic solution of the systems is given and the results in [1]~ [3],[7]~ [8]are c...In this paper,we consider the following systems x″+ Bx′+ gradG(x,t) = 0.Weak sufficient condition for the existence of a unique 2π-periodic solution of the systems is given and the results in [1]~ [3],[7]~ [8]are consequences of Theorem 2 in this paper if‖B‖2<1.展开更多
Barge asked if each homeomorphism of a hereditarily decomposable chainable continuum has zero topological entropy and Toledo asked if a homeomorphism of a chainable continuum can always be induced by square commuting ...Barge asked if each homeomorphism of a hereditarily decomposable chainable continuum has zero topological entropy and Toledo asked if a homeomorphism of a chainable continuum can always be induced by square commuting diagram on inverse systems of finite graphs. We show in this note that if Toledos question has a positive answer then Barges question also has a positive answer.展开更多
With the we of the homeomorphism theory and fixed point theory, the existence and uniqueness of solutions to boundary value problems are investigated. Two basic theorems are obtained without the boundness condition, w...With the we of the homeomorphism theory and fixed point theory, the existence and uniqueness of solutions to boundary value problems are investigated. Two basic theorems are obtained without the boundness condition, which generalizes results of Brown. When our results are applied to the existence and uniqueness of periodic solutions for nonlinear perturbed conservative systems (Newtonian equations of motion), the existence and uniqueness of the solution are obtained. The results in this note seem less restrictive than those of the former papers we have seen. Meanwhile, as far as we know, it seems that applying the homeomorphism theory to the research of this kind of problem is new.展开更多
The Beurling-Ahlfors’ extension is studied under relatively general conditions and its dilatation fonction is estimated. Particularly, the classic Deurling -Ahlfors’ theorem can be obtained under the M-condition.
This paper provides a regularity theorem for certain fourth-order differential operator Bλ with λ. from which we have obtained two homoeomorphism classes in 'nonlinear case' or three linear isomorphism clas...This paper provides a regularity theorem for certain fourth-order differential operator Bλ with λ. from which we have obtained two homoeomorphism classes in 'nonlinear case' or three linear isomorphism classes in 'linear case' about this operator respectively It is useful and convenient to explain certain types of stability properties in both directions of some flying vehiele in its moving process.展开更多
In this paper, a new set of sufficient conditions related to an initial value problem and global homeomorphism is obtained in discussing the existence and uniqueness of 2π-periodic solution for 2kth order differentia...In this paper, a new set of sufficient conditions related to an initial value problem and global homeomorphism is obtained in discussing the existence and uniqueness of 2π-periodic solution for 2kth order differential equations with resonance. The key role is played by nonnegative auxiliary scalar coercive function. The result of this paper generalizes some existed theorems.展开更多
In recent years, dynamical systems which are conjugate to their squares have been studied in ergodic theory. In this paper we study the consequences of groups having elements which are conjugate to their squares and c...In recent years, dynamical systems which are conjugate to their squares have been studied in ergodic theory. In this paper we study the consequences of groups having elements which are conjugate to their squares and consider examples arising from topological dynamics and more general dynamical展开更多
基金Supported by the National Natural Science Foundation of China(12201446)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(22KJB110005)the Shuangchuang Program of Jiangsu Province(JSSCBS20220898)。
文摘It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cylinder.By constructing a bounded solution of the monotone recurrence relation,the main conclusion in this paper is acquired:The induced homeomorphism has Birkhoff orbits provided there is a compact forward-invariant set.Therefore,it generalizes Angenent's results in low-dimensional cases.
文摘This paper provides a regularity theorem for certain 2nth-order differential operator Bλthat arises in considering some moving behaviors of certain objects, which includes (n + 2)homeomorphisms and extended homeomorphisms in 'real nonlinear case' or (n + 3) linearhomeomorphisms and extened linear homeomorphisms in 'complex linear case' for this operator. It is useful to illustrate some stabilities in both directions of certain objects in theirmoving processes.
基金The first author is supported by the Special Foundation of National Prior Basis Research of China(Grant No.G1999075108)the second author is supported by National Natural Science Foundation of China(11171320 and 11431012).
文摘In this paper we give a new and elementary proof to the following fact:each closed orientable surface of positive genus admits a both chaotic and expansive homeomorphism.Further more,we show that the homeomorphisms given are also weakly mixing.
文摘Let QS* (S 1) be the space of quasisymmetric homeomorphisms of the unit circle such that the corresponding subspace of the universal Teichmu¨ller space has Weil-Petersson metric.In this paper we give a necessary condition for a quasisymmetric homeomorphism to belong to QS *(S 1) from the aspect of cross-ratio distortion.
基金Supported partially by the Academy of Finland(Grant No.131477)the Magnus Ehrnrooth foundation
文摘Let f ： Ω→ f（Ω） belong to R^n be a W^1,1-homeomorphism with L^1-inegrable inner We show that finiteness of min{lipf（x）, kf（x））, for every x∈ Ω／E, implies that f^-1 ∈ W^1,n and has finite distortion, provided that the exceptional set E has σ-finite H^1-measure.Moreover, f has finite distortion, differentiable a.e. and the Jacobian Jf 〉 0 a.e.
基金Project supported by the National Natural Science Foundation of China and JTU
文摘Suppose that D is a domain in (n 2) and y= f(x): D → R^n is a homeomorphism. We prove that if the modulus dilatation K(x, f) satisfies the condition A then f(x) is ACL.
基金Supported by NSFC(Grant No.11201364)"the Fundamental Research Funds for the Central Universities"
文摘Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold BM, and fπ ： π1 （M）→π1 （M） be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the rank of the fixed subgroup of fπ, namely, rankFix（fπ） 〈 2rankπ1（M）, which is an analogue of inequalities on surface groups and hyperbolic 3-manifold groups.
基金Project supported by the National Natural Science Foundation of China(10361001)the Natural Science Foundation of the Committee of Education of Jiangshu Province (02KJB110008).
文摘We introduce the concept of asymptotic pseudo orbit tracing property (APOTP) and obtain a new condition by the APOTP for which a homeomor-phism is a non-wandering homeomorphism.
文摘Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r＋1/rα^r（α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.
基金partially supported by the Young Scientist Program of the Ministry of Science and Technology of China(2021YFA1002200)supported by National Natural Science Foundation of China(12101226)+1 种基金partially supported by the National Natural Science Foundation of China(12101362)supported by Shandong Provincial Natural Science Foundation(ZR2021QA032)。
文摘Let X be a Jordan domain satisfying certain hyperbolic growth conditions.Assume that φ is a homeomorphism from the boundary ?X of X onto the unit circle.Denote by h the harmonic diffeomorphic extension of φ from X onto the unit disk.We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of h.These generalize the Sobolev regularity of h in [A.Koski,J.Onninen,Sobolev homeomorphic extensions,J.Eur.Math.Soc.23(2021) 4065-4089,Theorem 3.1].
文摘In this paper,we consider the following systems x″+ Bx′+ gradG(x,t) = 0.Weak sufficient condition for the existence of a unique 2π-periodic solution of the systems is given and the results in [1]~ [3],[7]~ [8]are consequences of Theorem 2 in this paper if‖B‖2<1.
文摘Barge asked if each homeomorphism of a hereditarily decomposable chainable continuum has zero topological entropy and Toledo asked if a homeomorphism of a chainable continuum can always be induced by square commuting diagram on inverse systems of finite graphs. We show in this note that if Toledos question has a positive answer then Barges question also has a positive answer.
文摘With the we of the homeomorphism theory and fixed point theory, the existence and uniqueness of solutions to boundary value problems are investigated. Two basic theorems are obtained without the boundness condition, which generalizes results of Brown. When our results are applied to the existence and uniqueness of periodic solutions for nonlinear perturbed conservative systems (Newtonian equations of motion), the existence and uniqueness of the solution are obtained. The results in this note seem less restrictive than those of the former papers we have seen. Meanwhile, as far as we know, it seems that applying the homeomorphism theory to the research of this kind of problem is new.
文摘The Beurling-Ahlfors’ extension is studied under relatively general conditions and its dilatation fonction is estimated. Particularly, the classic Deurling -Ahlfors’ theorem can be obtained under the M-condition.
文摘This paper provides a regularity theorem for certain fourth-order differential operator Bλ with λ. from which we have obtained two homoeomorphism classes in 'nonlinear case' or three linear isomorphism classes in 'linear case' about this operator respectively It is useful and convenient to explain certain types of stability properties in both directions of some flying vehiele in its moving process.
基金Foundation item： Supported by the Natural Science Foundation of Changzhou Instituty of Technology（YN09090） Supported by the Natural Science Foundation of Jiangsu Province（13KJD110001）
文摘In this paper, a new set of sufficient conditions related to an initial value problem and global homeomorphism is obtained in discussing the existence and uniqueness of 2π-periodic solution for 2kth order differential equations with resonance. The key role is played by nonnegative auxiliary scalar coercive function. The result of this paper generalizes some existed theorems.
文摘In recent years, dynamical systems which are conjugate to their squares have been studied in ergodic theory. In this paper we study the consequences of groups having elements which are conjugate to their squares and consider examples arising from topological dynamics and more general dynamical
