*Vadim Kaloshin and Ke Zhang*

- Published in print:
- 2020
- Published Online:
- May 2021
- ISBN:
- 9780691202525
- eISBN:
- 9780691204932
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691202525.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was ...
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Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. This book provides the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. The book follows Mather's strategy but emphasizes a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, the book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.Less

Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. This book provides the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. The book follows Mather's strategy but emphasizes a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, the book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.

*P. J. E. Peebles*

- Published in print:
- 2020
- Published Online:
- May 2021
- ISBN:
- 9780691209838
- eISBN:
- 9780691206714
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691209838.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

An instant landmark on its publication, this book remains the essential introduction to this vital area of research. Written by one of the world's most esteemed theoretical cosmologists, it provides ...
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An instant landmark on its publication, this book remains the essential introduction to this vital area of research. Written by one of the world's most esteemed theoretical cosmologists, it provides an invaluable historical introduction to the subject, and an enduring overview of key methods, statistical measures, and techniques for dealing with cosmic evolution. With characteristic clarity and insight, the author focuses on the largest known structures — galaxy clusters — weighing the empirical evidence of the nature of clustering and the theories of how it evolves in an expanding universe. A must-have reference for students and researchers alike, this edition introduces a new generation of readers to a classic text in modern cosmology.Less

An instant landmark on its publication, this book remains the essential introduction to this vital area of research. Written by one of the world's most esteemed theoretical cosmologists, it provides an invaluable historical introduction to the subject, and an enduring overview of key methods, statistical measures, and techniques for dealing with cosmic evolution. With characteristic clarity and insight, the author focuses on the largest known structures — galaxy clusters — weighing the empirical evidence of the nature of clustering and the theories of how it evolves in an expanding universe. A must-have reference for students and researchers alike, this edition introduces a new generation of readers to a classic text in modern cosmology.

*P. J. E. Peebles*

- Published in print:
- 2020
- Published Online:
- May 2021
- ISBN:
- 9780691209814
- eISBN:
- 9780691206721
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691209814.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This book is the essential introduction to this critical area of modern physics, written by a leading pioneer who has shaped the course of the field for decades. The book provides an authoritative ...
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This book is the essential introduction to this critical area of modern physics, written by a leading pioneer who has shaped the course of the field for decades. The book provides an authoritative overview of the field, showing how observation has combined with theory to establish the science of physical cosmology. The book presents the elements of physical cosmology, including the history of the discovery of the expanding universe; surveys the cosmological tests that measure the geometry of space-time, with a discussion of general relativity as the basis for these tests; and reviews the origin of galaxies and the large-scale structure of the universe. Now featuring the author's 2019 Nobel lecture, the book remains an indispensable reference for students and researchers alike.Less

This book is the essential introduction to this critical area of modern physics, written by a leading pioneer who has shaped the course of the field for decades. The book provides an authoritative overview of the field, showing how observation has combined with theory to establish the science of physical cosmology. The book presents the elements of physical cosmology, including the history of the discovery of the expanding universe; surveys the cosmological tests that measure the geometry of space-time, with a discussion of general relativity as the basis for these tests; and reviews the origin of galaxies and the large-scale structure of the universe. Now featuring the author's 2019 Nobel lecture, the book remains an indispensable reference for students and researchers alike.

*P.J.E. Peebles*

- Published in print:
- 2019
- Published Online:
- May 2021
- ISBN:
- 9780691209821
- eISBN:
- 9780691206738
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691209821.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This book explains the often counterintuitive physics of quantum mechanics, unlocking this key area of physics for students by enabling them to work through detailed applications of general concepts ...
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This book explains the often counterintuitive physics of quantum mechanics, unlocking this key area of physics for students by enabling them to work through detailed applications of general concepts and ideas. The book states general principles first in terms of wave mechanics and then in the standard abstract linear space formalism. It offers a detailed discussion of measurement theory — an essential feature of quantum mechanics — and emphasizes the art of numerical estimates. Along the way, the book provides a wealth of physical examples together with numerous problems, some easy, some challenging, but all of them selected because they are physically interesting. The book is an essential resource for advanced undergraduates and beginning graduate students in physics.Less

This book explains the often counterintuitive physics of quantum mechanics, unlocking this key area of physics for students by enabling them to work through detailed applications of general concepts and ideas. The book states general principles first in terms of wave mechanics and then in the standard abstract linear space formalism. It offers a detailed discussion of measurement theory — an essential feature of quantum mechanics — and emphasizes the art of numerical estimates. Along the way, the book provides a wealth of physical examples together with numerous problems, some easy, some challenging, but all of them selected because they are physically interesting. The book is an essential resource for advanced undergraduates and beginning graduate students in physics.