In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of SU(2), U(2), SO(3), SO(3)×S^(1) and Spin ^(C)(3). We defin...In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of SU(2), U(2), SO(3), SO(3)×S^(1) and Spin ^(C)(3). We define the rotation vectors(numbers) of the left actions induced by the elements in the maximal tori of these groups, and utilize rotation vectors(numbers) to give the topologically conjugate classification of the left actions. Algebraic conjugacy and smooth conjugacy are also considered. As a by-product, we show that for any homeomorphism f : L(p,-1) × S^(1)→ L(p,-1) × S^(1), the induced isomorphism(π■f■i)_(*) maps each element in the fundamental group of L(p,-1) to itself or its inverse, where i : L(p,-1) → L(p,-1) × S^(1) is the natural inclusion and π : L(p,-1) × S^(1)→ L(p,-1) is the projection.展开更多
In this paper,a topological classification of piecewise monotone functions(abbreviated as PM functions)with nonmonotonicity height equal to 1 which are strictly increasing on their characteristic intervals and have fi...In this paper,a topological classification of piecewise monotone functions(abbreviated as PM functions)with nonmonotonicity height equal to 1 which are strictly increasing on their characteristic intervals and have finitely many fixed points is presented.展开更多
In this paper, several preimage entropies for semi-flows on compact metric spaces are introduced and studied. We prove that most of these entropies are invariant in a certain sense under conjugacy when the semi-flows ...In this paper, several preimage entropies for semi-flows on compact metric spaces are introduced and studied. We prove that most of these entropies are invariant in a certain sense under conjugacy when the semi-flows under consideration are free of fixed points. The relation between these entropies is studied and an inequality relating them is given. It is also shown that most of these entropies for semi-flow are consistent with that for the time-1 mapping.展开更多
In this paper, we show that a delayed discrete Hopfield neural network of two nonidentical neurons with no self-connections can demonstrate chaotic behavior in a region away from the origin. To this end, we first tran...In this paper, we show that a delayed discrete Hopfield neural network of two nonidentical neurons with no self-connections can demonstrate chaotic behavior in a region away from the origin. To this end, we first transform the model, by a novel way, into an equivalent system which enjoys some nice properties. Then, we identify a chaotic invariant set for this system and show that the system within this set is topologically conjugate to the full shift map on two symbols. This confirms chaos in the sense of Devaney. Our main result is complementary to the results in Kaslik and Balint (2008) and Huang and Zou (2005), where it was shown that chaos may occur in neighborhoods of the origin for the same system. We also present some numeric simulations to demonstrate our theoretical results.展开更多
Let ACD（M, SL（d,R）） denote the pairs （f, A） so that f∈ A C Diff^1（M） is a C^1-Anosov transitive diffeomorphisms and A is an SL（d,R） cocycle dominated with respect to f. We prove that open and densely in ACD...Let ACD（M, SL（d,R）） denote the pairs （f, A） so that f∈ A C Diff^1（M） is a C^1-Anosov transitive diffeomorphisms and A is an SL（d,R） cocycle dominated with respect to f. We prove that open and densely in ACD（M, SL（d,R））, in appropriate topologies, the pair （f,A） has simple spectrum with respect to the unique maximal entropy measure μf. Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in AUtLeb（M） × LP（M, SL（d, R））.展开更多
文摘In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of SU(2), U(2), SO(3), SO(3)×S^(1) and Spin ^(C)(3). We define the rotation vectors(numbers) of the left actions induced by the elements in the maximal tori of these groups, and utilize rotation vectors(numbers) to give the topologically conjugate classification of the left actions. Algebraic conjugacy and smooth conjugacy are also considered. As a by-product, we show that for any homeomorphism f : L(p,-1) × S^(1)→ L(p,-1) × S^(1), the induced isomorphism(π■f■i)_(*) maps each element in the fundamental group of L(p,-1) to itself or its inverse, where i : L(p,-1) → L(p,-1) × S^(1) is the natural inclusion and π : L(p,-1) × S^(1)→ L(p,-1) is the projection.
文摘In this paper,a topological classification of piecewise monotone functions(abbreviated as PM functions)with nonmonotonicity height equal to 1 which are strictly increasing on their characteristic intervals and have finitely many fixed points is presented.
基金the Tianyuan-Mathematics Foundation of China(10426012)the Doctoral Foundation of Hebei Normal University(L2005B02).
文摘In this paper, several preimage entropies for semi-flows on compact metric spaces are introduced and studied. We prove that most of these entropies are invariant in a certain sense under conjugacy when the semi-flows under consideration are free of fixed points. The relation between these entropies is studied and an inequality relating them is given. It is also shown that most of these entropies for semi-flow are consistent with that for the time-1 mapping.
基金National Natural Science Foundation of China (Grant Nos. 11071263 and 11201504)the Natural Sciences and Engineering Research Council of Canada (Grant No. 227048-2010)
文摘In this paper, we show that a delayed discrete Hopfield neural network of two nonidentical neurons with no self-connections can demonstrate chaotic behavior in a region away from the origin. To this end, we first transform the model, by a novel way, into an equivalent system which enjoys some nice properties. Then, we identify a chaotic invariant set for this system and show that the system within this set is topologically conjugate to the full shift map on two symbols. This confirms chaos in the sense of Devaney. Our main result is complementary to the results in Kaslik and Balint (2008) and Huang and Zou (2005), where it was shown that chaos may occur in neighborhoods of the origin for the same system. We also present some numeric simulations to demonstrate our theoretical results.
基金Supported by FCT-Fundao para a Ciência e a Tecnologia and CNPq-Brazil(Grant No.PEst-OE/MAT/UI0212/2011)
文摘Let ACD（M, SL（d,R）） denote the pairs （f, A） so that f∈ A C Diff^1（M） is a C^1-Anosov transitive diffeomorphisms and A is an SL（d,R） cocycle dominated with respect to f. We prove that open and densely in ACD（M, SL（d,R））, in appropriate topologies, the pair （f,A） has simple spectrum with respect to the unique maximal entropy measure μf. Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in AUtLeb（M） × LP（M, SL（d, R））.
