This paper studies the dynamics of the family λ sin z for some values of λ. First we give a description of the Fatou set for values of λ inside the unit disc. Then for values of λ on the unit circle of parabolic type (λ = exp(i2πθ), θ = p/q, (p, q) = 1), we prove that if q is even, there is one q-cycle of Fatou components, if q is odd, there are two q cycles of Fatou components. Moreover the Fa...

We explore the connected/disconnected dichotomy for the Julia set of polynomial automorphisms of C. We develop several aspects of the question, which was first studied by Bedford-Smillie [BS6, BS7]. We introduce a new sufficient condition for the connectivity of the Julia set, that carries over for certain Hénon-like and birational maps. We study the structure of disconnected Julia sets and the...

The moduli space Mg of compact Riemann surfaces of genus g has structure of orbifold and the set of singular points for such orbifold is the branch locus Bg. In this article we present some results related with the topology of Bg, the connectedness of Bg for g ≤ 8, the existence of isolated equisymmetric strata of a given dimension in Bg and finally the connectedness of the branch locus of the ...

1. The Parameter Space for Cubic Maps 2. Real Cubic Maps as Real Dynamical Systems 3. Complex Cubics: The Connectedness Locus 4. Hyperbolic Components Appendix A. Normal Forms and Curves in Parameter Space Appendix B. Centers of Some Hyperbolic Components Appendix C. Comments on the Figures References This article discusses the dynamics of iterated cubic maps from the real or complex line to it...

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 CHAPTER I. Univalent functions in complex analytic dynamics . . . . . . 147 1. Attraction to infinity . . . . . . . . . . . . . . . . . . . . . . . 147 2. Parametrizing the space of polynomials . . . . . . . . . . . . . 150 3. Compactness of the connectedness locus . . . . . . . . . . . . 153 4. The mapping q~e is ...

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Currently, connectedness assesment is primarily done through questionnaires. Although questionnaires are good for tapping into the user experience, they also have drawbacks, like memory biases, proneness to social masking, and lack of mental access. Now that sophisticated sensors are becoming cheaper, less obtrusive, and more widely available, this opens doors to more objective continuous measu...

Debates about academic freedom have become increasingly fierce and frequent. Legislative efforts to regulate American professors proliferate across the nation. Although most American scholars desire to pages: 272 Solidarity as they have emerged in particular fiscal problems this together cracking open. And what do we would have to say that professors need just. She can refer to accept the capit...

Economic connectedness can be defined as the degree of internal connectedness of interdependence between the sectors of an economy. In input-output models intersectoral connectedness is a crucial feature of analysis, and there are many different methods of measuring it. These measures are believed to be important structural indicators, helpful in model estimation. Also, such measures could be a...