Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices has been used quite a lot for master and PhD courses. All chapters are concluded by an exercise section. The book is also directed towards researchers, where one of the challenges is to help applied researchers acquire background for a better understanding of the data that computer simulation or experiment may provide them with the development of the theory.
The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.
Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices has been used quite a lot for master and PhD courses. All chapters are concluded by an exercise section. The book is also directed towards researchers, where one of the challenges is to help applied researchers acquire background for a better understanding of the data that computer simulation or experiment may provide them with the development of the theory.
The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.
Near the Horizon starts out by considering several optical phenomena that can occur when the sun is near the horizon. One can sometimes see objects that are actually below the horizon. Sometimes there seems to be a dark strip in the middle of the solar disk. These are a result of the way that the atmosphere affects the geometry of light rays. Broer starts his book with the Fermat principle (rays of light take least-time paths) and deduces from it laws for refraction and reflection; by expressing these as conservation laws, he can handle both the case of inhomogeneous layers of air and the case of continuous variation in the refraction index. A surprising application is the brachistochrone problem, in which the path of fastest descent is determined by studying how a light ray would behave in a “flat earth” atmosphere whose refraction index is determined by the gravitational potential. This leads to a very interesting chapter on the cycloid and its properties. The final chapters move from the elementary theory to a more sophisticated version in which the Fermat Principle leads to a Riemannian metric whose geodesics are the paths of light rays. This gives us an optics which is geometric in a new sense, and serves as a nice demonstration of the physical applicability of Riemannian geometry.
From the nineteen sixties onwards a branch of philosophy of science has come to development, called history-oriented philosophy of science. This development constitutes a reaction on the then prevailing logical empiricist conception of scientific knowledge. The latter was increasingly seen as suffering from insurmountable internal problems, like e. g. the problems with the particular "observational-theoretical distinction" on which it drew. In addition the logical empiricists' general approach was increasingly criticized for two external shortcomings. Firstly, the examples of scientific knowledge that the logical empiricists were focusing on were con sidered as too simplistic to be informative on the nature of real life science. Secondly, it was felt that the attention of these philosophers of science was restricted to the static aspects of scientific knowledge, while neglecting its developmental aspects. History-oriented philosophy of science has taken up the challenge implicit in the latter two criticisms, i. e. to develop accounts of science that would be more adequate for understanding the development 1 of real life science. One of the more successful products of this branch of philosophy of science is Lakatos's theory of scientific development, sometimes called the "methodology of scientific research programmes". This theory conceives science as consisting of so called research program mes developing in time, and competing with each other over the issue which one generates the best explan~tions of the phenomena that they address.
This book presents stochastic dynamical systems theory in order to synthesize our current knowledge of climate variability, for graduate students and researchers.
Silver-grey manpower is a gold mine to society. One by one, the baby boom cohorts will reach the age of 65 starting from 2010. They are large cohorts, relatively well educated and healthy with considerable pension and health care rights. In short, they are lucky devils. As a result of ageing, cohorts that were born in 1985 onwards and that enter the labour market as from approximately 2010 will be required to pay many additional taxes during the course of their entire working life spanning more than forty years. They are, in short, unlucky dogs. Redistribution of joys and burdens could trigger conflicts between generations. A better solution is to identify and deploy society’s hidden resources. Taking this issue as a basis, the book in hand explores strategies that enable senior citizens and young people to give meaning to solidarity among generations, for a start in 2012 as the European Year for Active Ageing, but also as part of Europe 2020, the European Commission’s 2010-2020 strategy. With these two strategies journalists and television producers will swing into action. In secondary and higher education as well as in universities more papers on life courses and patterns of generations will be written than ever before. Senior citizens’ unions but actually all social organizations will organize lectures. Educated laymen will wish to go deeply into this issue. Henk A. Becker (1933) is Professor Emeritus of Sociology at Utrecht University in the Netherlands. He has worked on a research project focusing on generations since 1985.
The architecture of the human language faculty has been one of the main foci of the linguistic research of the last half century. This branch of linguistics, broadly known as Generative Grammar, is concerned with the formulation of explanatory formal accounts of linguistic phenomena with the ulterior goal of gaining insight into the properties of the 'language organ'. The series comprises high quality monographs and collected volumes that address such issues. The topics in this series range from phonology to semantics, from syntax to information structure, from mathematical linguistics to studies of the lexicon. To discuss your book idea or submit a proposal, please contact Birgit Sievert
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