Dynamics of composite functions meromorphic outside a small set

AbstractLet M denote the class of functions f meromorphic outside some compact totally disconnected set E=E(f) and the cluster set of f at any a∈E with respect to Ec=Cˆ\E is equal to Cˆ. It is known that class M is closed under composition. Let f and g be two functions in class M, we study relationship between dynamics of f○g and g○f. Denote by F(f) and J(f) the Fatou and Julia sets of f. Let U be a component of F(f○g) and V be a component of F(g○f) which contains g(U). We show that under certain conditions U is a wandering domain if and only if V is a wandering domain; if U is periodic, then so is V and moreover, V is of the same type according to the classification of periodic components as U unless U is a Siegel disk or Herman ring

New Delay-Range-Dependent Robust Exponential Stability Criteria of Uncertain Impulsive Switched Linear Systems with Mixed Interval Nondifferentiable Time-Varying Delays and Nonlinear Perturbations

We investigate the problem of robust exponential stability analysis for uncertain impulsive switched linear systems with time-varying delays and nonlinear perturbations. The time delays are continuous functions belonging to the given interval delays, which mean that the lower and upper bounds for the time-varying delays are available, but the delay functions are not necessary to be differentiable. The uncertainties under consideration are nonlinear time-varying parameter uncertainties and norm-bounded uncertainties, respectively. Based on the combination of mixed model transformation, Halanay inequality, utilization of zero equations, decomposition technique of coefficient matrices, and a common Lyapunov functional, new delay-range-dependent robust exponential stability criteria are established for the systems in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed method

Teaching Instrumental Science Globally Using a Collaborative Electronic Laboratory Notebook

In the higher education sector there is a strong push to improve the synergy between research and teaching. To achieve this there is a need to introduce into the undergraduate curriculum the new technologies that support research practice and process. There is no doubt that future scientific practice will increasingly involve collaborations around data and information that is delivered via the web. Our students must be trained in these new developments, and our staff must have access to tools that will facilitate their ability to teach it. New technologies, such as the Electronic Laboratory Notebook (ELN) developed at Southampton University in the UK, exploits the Web2.0 environment and offer the advantages of 1) being able to more readily share research resources, 2) as a digital record of experimental events and 3) a secure archive of data and metadata. We will discuss our initiative to extend the science curriculum in undergraduate chemistry through the introduction of an electronic laboratory notebook where instruments, experiments and data can be shared globally. The ELN is presently being implemented at UNSW, and the proposed project (funded by the Australian Learning and Teaching Council) will allow a multi-university (three in Australia, one in Thailand and one in the UK) exemplar of the ELN. By its nature, the project the outcomes will be available worldwide for tertiary science training. Keywords: electron laboratory notebook, science education, eResearch, eLearnin

Dynamics of Newton's functions of Barna's polynomials

We define Barna's polynomials as real polynomials with all real roots of which at least four are distinct. In this paper, we study the dynamics of Newton's functions of such polynomials. We also give the upper and lower bounds of the Hausdorff dimension of exceptional sets of these Newton's functions

A characterization of Möbius transformations

We give a new invariant characteristic property of Möbius transformations

Julia Sets and Symbolic Dynamics of Certain Rational and Entire Functions

77 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997.A complex analytic map f always decomposes the complex plane into two dis-joint subsets, the Julia set J(f) on which the family of iterates of f, \{f\sp{k}\}\sbsp{k=0}{\infty}, fails to be a normal family, and its complement, the Fatou set F(f). The dynamics of f on its Fatou set is relatively tame while the dynamics on its Julia set is always complicated. We study the Julia sets and Symbolic dynamics of certain rational and entire functions. We also estimate the size of some Julia sets in terms of their Hausdorff dimension.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD