The chaotic properties of some subshift maps are investigated. These subshifts are the orbit closures of certain non-periodic recurrent points of a shift map. We first provide a review of basic concepts for dynamics of continuous maps in metric spaces. These concepts include nonwandering point, recurrent point, eventually periodic point, scrambled set, sensitive dependence on initial conditions...

5 The Variational principles and periodic orbits 21 5.1 Lagrangian view point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2 Hamiltonian view point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.3 Fixed energy problem, the Hill’s region . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.4 Continuation of periodic orbits as critical p...

We show the existence of an infinite monothetic Polish topological group G with the fixed point on compacta property. Such a group provides a positive answer to a question of Mitchell who asked whether such groups exist, and a negative answer to a problem of R. Ellis on the isomorphism of L(G), the universal point transitive G-system (for discrete G this is the same as PG the Stonetech compacti...

In this paper, based on the properties of almost periodic function and exponential dichotomy of linear system on time scales as well as Krasnoselskii’s fixed point theorem, some sufficient conditions are established for the existence of square-mean almost periodic solutions of neutral stochastic functional differential equations on time scales. Finally, an example is presented to illustrate the...

We study convergence group actions on continua, and give a criterion which ensures that every global cut point is a parabolic fixed point. We apply this result to the case of boundaries of relatively hyperbolic groups, and consider implications for connectedness properties of such spaces.

In this paper, we prove the existence and uniqueness of fixed points for cyclic (α,β)-admissible type F-contraction and F−weak contraction under the setting of modular spaces, where the modular is convex and satisfying the ∆2-condition. Later, we prove some periodic point results for self-mappings on a modular space. We also give some examples to s...

In this paper, we consider a class of boundary value problems of fractional differential equations with integral and anti-periodic boundary conditions, which is a new type of mixed boundary condition. By using the contraction mapping principle, Krasnosel’skii fixed point theorem, and Leray-Schauder degree theory, we obtain some results of existence and uniqueness. Finally, several examples are ...

In this paper using the well-known Schauder fixed point theorem we study and obtain the existence of almost periodic mild solutions to some classes of nonautonomous third-order differential equations on a separable infinite dimensional complex Hilbert space.

*Correspondence: [email protected] 1School of Mathematical Science and Computing Technology, Central South University, Changsha, Hunan 410075, P.R. China 2School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410076, P.R. China Full list of author information is available at the end of the article Abstract By using Schauder’s fixed poin...

This paper introduces the concept of square-mean piecewise almost periodic for impulsive stochastic processes. The existence of square-mean piecewise almost periodic solutions for linear and nonlinear impulsive stochastic differential equations is established by using the theory of the semigroups of the operators and Schauder fixed point theorem. The stability of the square-mean piecewise almos...