We prove that there exists an open and dense subset U in the space of C^(2) expanding self-maps of the circle T such that the Lyapunov minimizing measures of any T∈U are uniquely supported on a periodic orbit.This an...We prove that there exists an open and dense subset U in the space of C^(2) expanding self-maps of the circle T such that the Lyapunov minimizing measures of any T∈U are uniquely supported on a periodic orbit.This answers a conjecture of Jenkinson-Morris in the C^(2) topology.展开更多
In this paper,we propose a new method to study intermittent behaviors of coupled piecewise-expanding map lattices.We show that the successive transition between ordered and disordered phases occurs for almost every or...In this paper,we propose a new method to study intermittent behaviors of coupled piecewise-expanding map lattices.We show that the successive transition between ordered and disordered phases occurs for almost every orbit when the coupling is small.That is,lim inf n→∞∑1≤i,j≤m|x_(i)(n)−x_(j)(n)|=0,lim sup n→∞∑1≤i,j≤m|x_(i)(n)−x_(j)(n)|≥c_(0)>0,where xi(n)correspond to the coordinates of m nodes at the iterative step n.Moreover,when the uncoupled system is generated by the tent map and the lattice consists of two nodes,we prove a phase transition occurs between synchronization and intermittent behaviors.That is,limn→∞|x_(1)(n)−x_(2)(n)|=0 for c−1/2<1/4 and intermittent behaviors occur for|c−1/2|>1/4,where 0≤c≤1 is the coupling.展开更多
In this paper, we give a criterion of whether there are non-wandering expanding maps on a given branched 1-manifold. As an application, we give an example of a dynamic on a 3-manifold having non-zero first Betti numbe...In this paper, we give a criterion of whether there are non-wandering expanding maps on a given branched 1-manifold. As an application, we give an example of a dynamic on a 3-manifold having non-zero first Betti number, the non-wander sets of which are two Smale–Williams solenoids.展开更多
In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are...In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions （m → 1）. This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.展开更多
In this paper, we deal with one-parameter families of real cellular automata in R2. We prove that for a wide class of block functions from R2 to R, the corresponding real cellular automaton is expanding when the value...In this paper, we deal with one-parameter families of real cellular automata in R2. We prove that for a wide class of block functions from R2 to R, the corresponding real cellular automaton is expanding when the value of the parameter is large enough.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11501391)the Scientific Research Project of Sichuan University of Science and Engineering(Grant No.2014RC02)
文摘In this paper, it is proved that a nonuniformly expanding map f having the dshadowing property or d-shadowing property is topologically transitive.
基金partially supported by National Key R&D Program of China(Grant Nos.2022YFA1005801)NSFC(Grant Nos.12171348,12325106,ZXL2024386)+2 种基金partially supported by NSFC(Grant Nos.12090012,12031019,11731003)partially supported by NSFC(Grant Nos.12031019,11801538,11871188)Jiangsu Specially Appointed Professorship。
文摘We prove that there exists an open and dense subset U in the space of C^(2) expanding self-maps of the circle T such that the Lyapunov minimizing measures of any T∈U are uniquely supported on a periodic orbit.This answers a conjecture of Jenkinson-Morris in the C^(2) topology.
基金This work is supported by NSFC of China(Grants Nos.11031003,11271183,11971105 and 11771205)and Simons Foundation.
文摘In this paper,we propose a new method to study intermittent behaviors of coupled piecewise-expanding map lattices.We show that the successive transition between ordered and disordered phases occurs for almost every orbit when the coupling is small.That is,lim inf n→∞∑1≤i,j≤m|x_(i)(n)−x_(j)(n)|=0,lim sup n→∞∑1≤i,j≤m|x_(i)(n)−x_(j)(n)|≥c_(0)>0,where xi(n)correspond to the coordinates of m nodes at the iterative step n.Moreover,when the uncoupled system is generated by the tent map and the lattice consists of two nodes,we prove a phase transition occurs between synchronization and intermittent behaviors.That is,limn→∞|x_(1)(n)−x_(2)(n)|=0 for c−1/2<1/4 and intermittent behaviors occur for|c−1/2|>1/4,where 0≤c≤1 is the coupling.
文摘In this paper, we give a criterion of whether there are non-wandering expanding maps on a given branched 1-manifold. As an application, we give an example of a dynamic on a 3-manifold having non-zero first Betti number, the non-wander sets of which are two Smale–Williams solenoids.
基金Project supported by the Anhui Key Laboratory of Information Materials and Devices (Anhui University),China
文摘In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions （m → 1）. This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.
文摘In this paper, we deal with one-parameter families of real cellular automata in R2. We prove that for a wide class of block functions from R2 to R, the corresponding real cellular automaton is expanding when the value of the parameter is large enough.
