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Understanding the earth system : global change science for application
\"Explaining the what, the how and the why of climate science, this multidisciplinary new book provides a review of research from the last decade, illustrated with cutting-edge data and observations. A key focus is the development of analysis tools that can be used to demonstrate options for mitigating and adapting to increasing climate risks. Emphasis is given to the importance of Earth system feedback mechanisms and the role of the biosphere. The book explains advances in modelling, process understanding and observations, and the development of consistent and coherent studies of past, present and 'possible' climates. This highly-illustrated, data-rich book is written by leading scientists involved in QUEST, a major UK-led research programme. It forms a concise and up-to-date reference for academic researchers or students in the fields of climatology, Earth system science and ecology, and also a vital resource for professionals and policymakers working on any aspect of global change\"-- Provided by publisher.
Book
Spectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows
In this work we study strong spectral properties of Ruelle transfer operators related to a large family of Gibbs measures for contact
Anosov flows. The ultimate aim is to establish exponential decay of correlations for Hölder observables with respect to a very general
class of Gibbs measures. The approach invented in 1997 by Dolgopyat in “On decay of correlations in Anosov flows” and further developed
in Stoyanov (2011) is substantially refined here, allowing to deal with much more general situations than before, although we still
restrict ourselves to the uniformly hyperbolic case. A rather general procedure is established which produces the desired estimates
whenever the Gibbs measure admits a Pesin set with exponentially small tails, that is a Pesin set whose preimages along the flow have
measures decaying exponentially fast. We call such Gibbs measures regular. Recent results in Gouëzel and Stoyanov (2019) prove existence
of such Pesin sets for hyperbolic diffeomorphisms and flows for a large variety of Gibbs measures determined by Hölder continuous
potentials. The strong spectral estimates for Ruelle operators and well-established techniques lead to exponential decay of correlations
for Hölder continuous observables, as well as to some other consequences such as: (a) existence of a non-zero analytic continuation of
the Ruelle zeta function with a pole at the entropy in a vertical strip containing the entropy in its interior; (b) a Prime Orbit
Theorem with an exponentially small error.
eBook
Symbolic Extensions of Amenable Group Actions and the Comparison Property
In topological dynamics, the
Of course, the statement is preceded by the
presentation of the concepts of an entropy structure and its superenvelopes, adapted from the case of
eBook
Conformal Graph Directed Markov Systems on Carnot Groups
We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped
with a sub-Riemannian metric. In particular, we develop the thermodynamic formalism and show that, under natural hypotheses, the limit
set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen’s parameter. We illustrate our results for a variety of examples
of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include
the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the
non-real classical rank one hyperbolic spaces.
eBook
A billion butterflies : a life in climate and chaos theory
\"The amazing true story of the man behind modern weather prediction. Consider a world without weather prediction. How would we know when to evacuate communities ahead of fires or floods, or figure out what to wear tomorrow? Until 40 years ago, we couldn't forecast weather conditions beyond ten days. Renowned climate scientist Dr. Jagadish Shukla is largely to thank for modern weather forecasting. Born in rural India with no electricity, plumbing, or formal schools, he attended classes that were held in a cow shed. Shukla grew up amid turmoil: overwhelming monsoons, devastating droughts, and unpredictable crop yields. His drive brought him to the Indian Institute of Tropical Meteorology, despite little experience. He then followed an unlikely path to MIT and Princeton, and the highest echelons of climate science. His work, which has enabled us to predict weather farther into the future than previously thought possible, allows us to feed more people, save lives, and hold on to hope in a warming world. Paired with his philanthropic endeavors and extreme dedication to the field, Dr. Shukla has been lauded internationally for his achievements, including a shared Nobel Peace Prize with Al Gore for his governmental research on climate change. A Billion Butterflies is a wondrous insider's account of climate science and an unbelievable memoir of his life. Understanding dynamical seasonal prediction will change the way you experience a thunderstorm or interpret a forecast; understanding its origins and the remarkable story of the man who discovered it will change the way you see our world\"-- Provided by publisher.
BOOK
Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume
We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We
then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of
eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume
and the dynamics of their geodesic flows.
eBook
Thermodynamics
This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics. The authors' theory is motivated by the fact that a discipline as cardinal as thermodynamics--entrusted with some of the most perplexing secrets of our universe--demands far more than physical mathematics as its underpinning. Even though many great physicists, such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, this book suggests that a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth. This book uses system theoretic ideas to bring coherence, clarity, and precision to an extremely important and poorly understood classical area of science.
eBook