This volume clearly reflects Ricardo Mane's legacy, his contribution to mathematics and the diversity of his mathematical intersts. It contains fifteen refereed research papers on thems including Hamiltonian and Lagrangian dynamics, growth rate of the number of geodesics on a compact manifold, one dimensional complex and real dynamics, and bifurcations and singular cycles. This book also contains two famous sets of notes by Ricardo Mane. One is the seminal paper on Lagrangian dynamics that he had prepared for the conference; the other is on the genericity of zero exponents area preserving diffeomorphisms on surfaces when non Anosov. This book will be of particular interest to researchers and graduate students in mathematics, mechanics and mathematical physics.
This book argues that new developments in the sciences, in particular twentieth-century physics and twenty-first-century biology, suggest revising several pessimistic outlooks for the development of a scientific understanding of the relationship of humans with the universe - in particular, implications for the development of a natural religiousness. In the new vision a universe which is friendly to life and consciousness naturally emerges.
What is consciousness? Does free will exist?There exists a widespread conviction that the recent scientific discoveries, especially those related to physics and biology, in particular in contemporary neurosciences, question the traditional attempts to give meaning to life and a basis for our moral compass. Current scientific thinking usually identifies the mind with the mere exchange of electrical signals among neurons. It claims that consciousness is an irrelevant epiphenomenon and that introspection is an unreliable instrument to achieve any form of knowledge. Also, that the physical universe is causally closed and therefore all that occurs only has physical causes and all kind of freedom is excluded. The problem of assigning meaning and purpose to our lives, to the essential conceptions of the value of human life and social justice, becomes practically insoluble if one accepts the predominant notions that supposedly stem from contemporary science. The clash between the scientific and humanistic conception of human beings seems to have no option but to abandon the latter.The aim of this book is to show that, contrary to what is usually considered, current advances in science allow to re-evaluate the role of consciousness and human freedom without entering into contradiction with empirical evidence or scientific theories in place today. The book starts by analyzing the certainties provided by the scientific thought and philosophical reflection while discussing the role and content of physical theories, and in particular, quantum mechanics. It discusses in detail the nature of quantum objects and the role they may have in consciousness. In particular, it analyzes models that allow phenomena of quantum nature to manifest themselves in the brains of animals and humans, and account for many of the properties of consciousness. Finally, we analyze how self-conscious and free entities like persons emerge, making compatible the scientific view with a renewed and better supported way of perceiving people, their values and culture.
This book is devoted to the frequency domain approach, for both regular and degenerate Hopf bifurcation analyses. Besides showing that the time and frequency domain approaches are in fact equivalent, the fact that many significant results and computational formulas obtained in the studies of regular and degenerate Hopf bifurcations from the time domain approach can be translated and reformulated into the corresponding frequency domain setting, and be reconfirmed and rediscovered by using the frequency domain methods, is also explained. The description of how the frequency domain approach can be used to obtain several types of standard bifurcation conditions for general nonlinear dynamical systems is given as well as is demonstrated a very rich pictorial gallery of local bifurcation diagrams for nonlinear systems under simultaneous variations of several system parameters. In conjunction with this graphical analysis of local bifurcation diagrams, the defining and nondegeneracy conditions for several degenerate Hopf bifurcations is presented. With a great deal of algebraic computation, some higher-order harmonic balance approximation formulas are derived, for analyzing the dynamical behavior in small neighborhoods of certain types of degenerate Hopf bifurcations that involve multiple limit cycles and multiple limit points of periodic solutions. In addition, applications in chemical, mechanical and electrical engineering as well as in biology are discussed. This book is designed and written in a style of research monographs rather than classroom textbooks, so that the most recent contributions to the field can be included with references.
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