Marcelo Viana's Books

Differential Equations

A Dynamical Systems Approach to Theory and Practice

By: Marcelo Viana,José M. Espinar

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Differential Equations

A Dynamical Systems Approach to Theory and Practice

By: Marcelo Viana,José M. Espinar

This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincaré's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our time—pure and applied alike—ought to learn. The book features a dynamical perspective that drives the motivating questions, the style of exposition, and the arguments and proof techniques. The text is organized in six cycles. The first cycle deals with the foundational questions of existence and uniqueness of solutions. The second introduces the basic tools, both theoretical and practical, for treating concrete problems. The third cycle presents autonomous and non-autonomous linear theory. Lyapunov stability theory forms the fourth cycle. The fifth one deals with the local theory, including the Grobman–Hartman theorem and the stable manifold theorem. The last cycle discusses global issues in the broader setting of differential equations on manifolds, culminating in the Poincaré–Hopf index theorem. The book is appropriate for use in a course or for self-study. The reader is assumed to have a basic knowledge of general topology, linear algebra, and analysis at the undergraduate level. Each chapter ends with a computational experiment, a diverse list of exercises, and detailed historical, biographical, and bibliographic notes seeking to help the reader form a clearer view of how the ideas in this field unfolded over time.

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Page Count

536

Publisher

American Mathematical Society

Published Date

ISBN 10

147046540X

ISBN 13

9781470465407

Dynamics Beyond Uniform Hyperbolicity

A Global Geometric and Probabilistic Perspective

By: Christian Bonatti,Lorenzo J. Díaz,Marcelo Viana

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Dynamics Beyond Uniform Hyperbolicity

A Global Geometric and Probabilistic Perspective

By: Christian Bonatti,Lorenzo J. Díaz,Marcelo Viana

What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an "infinitesimal" evolution rule is known. Examples and applications arise from all branches of science and technology, like physics, chemistry, economics, ecology, communications, biology, computer science, or meteorology, to mention just a few. These systems have in common the fact that each possible state may be described by a finite (or infinite) number of observable quantities, like position, velocity, temperature, concentration, population density, and the like. Thus, m the space of states (phase space) is a subset M of an Euclidean space M . Usually, there are some constraints between these quantities: for instance, for ideal gases pressure times volume must be proportional to temperature. Then the space M is often a manifold, an n-dimensional surface for some n

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Page Count

390

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540268448

ISBN 13

9783540268444

Foundations of Ergodic Theory

By: Marcelo Viana,Krerley Oliveira

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Foundations of Ergodic Theory

By: Marcelo Viana,Krerley Oliveira

Self-contained introductory textbook suitable for a variety of one- or two-semester courses. Rich with examples, applications and exercises.

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Page Count

547

Publisher

Cambridge University Press

Published Date

ISBN 10

1107126967

ISBN 13

9781107126961

Chains of Gold

Portuguese Migration to Argentina in Transatlantic Perspective

By: Marcelo Borges

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Chains of Gold

Portuguese Migration to Argentina in Transatlantic Perspective

By: Marcelo Borges

Why did migrants from southern Portugal choose Argentina instead of following the traditional path to Brazil? Starting with this question, this book explores how, at the turn of the twentieth century, rural Europeans developed distinctive circuits of transatlantic labor migration linked to diverse immigrant communities in the Americas. It looks at transoceanic moves in the larger context of migration systems, examining their connections and the crucial role of social networks in migrants’ geographic mobility and adaptation. Combining regional and local perspectives on both sides of the Atlantic, Chains of Gold provides a vivid account of the trajectories of migrant men and women as they moved from rural Portugal to contrasting places of settlement in the Argentine pampas and Patagonia.

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Page Count

369

Publisher

BRILL

Published Date

ISBN 10

9047429923

ISBN 13

9789047429920

Laborers and Enslaved Workers

Experiences in Common in the Making of Rio de Janeiro's Working Class, 1850-1920

By: Marcelo Badaró Mattos

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Laborers and Enslaved Workers

Experiences in Common in the Making of Rio de Janeiro's Working Class, 1850-1920

By: Marcelo Badaró Mattos

From the middle of the nineteenth century until the 1888 abolition of slavery in Brazil, Rio de Janeiro was home to the largest urban population of enslaved workers anywhere in the Americas. It was also the site of an incipient working-class consciousness that expressed itself across seemingly distinct social categories. In this volume, Marcelo Badaró Mattos demonstrates that these two historical phenomena cannot be understood in isolation. Drawing on a wide range of historical sources, Badaró Mattos reveals the diverse labor arrangements and associative life of Rio’s working class, from which emerged the many strategies that workers both free and unfree pursued in their struggles against oppression.

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