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Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

Alfonso Sorrentino

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164502
eISBN:
9781400866618
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164502.001.0001
Subject:
Mathematics, Applied Mathematics

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical ... More


Puritan New England and the Foundations of the American Jeremiad

Andrew R. Murphy

in Prodigal Nation: Moral Decline and Divine Punishment from New England to 9/11

Published in print:
2008
Published Online:
January 2009
ISBN:
9780195321289
eISBN:
9780199869855
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195321289.003.0002
Subject:
Religion, Religion and Society

This chapter provides an in‐depth exploration of the jeremiad in second‐generation New England (c.1660–1685). Delivered primarily in the form of election or fast day sermons, the New England jeremiad ... More


Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

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 ... More


Augustan American Literature: An Aesthetics of Extravagance

Paul Giles

in The Global Remapping of American Literature

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691136134
eISBN:
9781400836512
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691136134.003.0002
Subject:
Literature, Criticism/Theory

This chapter examines the Augustan tradition in American literature, arguing that it should not be seen as confined to the world of belles lettres. It suggests that Augustan American literature ... More


The Hamilton-Jacobi Equation and Weak KAM Theory

Alfonso Sorrentino

in Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164502
eISBN:
9781400866618
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164502.003.0005
Subject:
Mathematics, Applied Mathematics

This chapter describes another interesting approach to the study of invariant sets provided by the so-called weak KAM theory, developed by Albert Fathi. This approach can be considered as the ... More


Theology in Colonial America

Mark A. Noll

in America's God: From Jonathan Edwards to Abraham Lincoln

Published in print:
2002
Published Online:
November 2003
ISBN:
9780195151114
eISBN:
9780199834532
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195151119.003.0002
Subject:
Religion, History of Christianity

Theologians dominated the public square in Colonial America. Colonial American theology in many ways maintained continuity with Old World understandings of the world and the church. Colonial ... More


Landfall: The New World as New Creation

John Gatta

in Making Nature Sacred: Literature, Religion, and the Environment in America from the Puritans to the Present

Published in print:
2004
Published Online:
January 2005
ISBN:
9780195165050
eISBN:
9780199835140
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195165055.003.0002
Subject:
Religion, Religion and Literature

During the colonial era, British settlers only gradually allowed North America’s actual physical environment to shape their idea of the New World they inhabited. Although New England Puritans were ... More


Law and the Utopian Imagination

Austin Sarat, Lawrence Douglas, and Martha Merill Umphrey (eds)

Published in print:
2014
Published Online:
September 2014
ISBN:
9780804790819
eISBN:
9780804791861
Item type:
book
Publisher:
Stanford University Press
DOI:
10.11126/stanford/9780804790819.001.0001
Subject:
Law, Philosophy of Law

This book is a project of exploration and resuscitation of idea of utopianism within legal discourse. Instead of mapping out the contours of a familiar terrain, the contributors seek to explore the ... More


Policing the Borders, or, How Independent Ministers Rode the Canonical Range

David F. Holland

in Sacred Borders: Continuing Revelation and Canonical Restraint in Early America

Published in print:
2011
Published Online:
May 2011
ISBN:
9780199753611
eISBN:
9780199895113
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199753611.003.0002
Subject:
Religion, History of Christianity

This chapter opens with a discussion of the Anglican Book of Common Prayer and explores the reasons why Puritans criticized the book as a violation of the closed canon. It considers the role of ... More


The Puritans: Celebrating the Glory of Heaven

Gary Scott Smith

in Heaven in the American Imagination

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199738953
eISBN:
9780199897346
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199738953.003.0002
Subject:
Religion, History of Christianity

More than most other American Christians, the Puritans lived with one eye on eternity. Especially as put forth by Increase Mather, the Puritan conception of heaven was theocentric, focusing on the ... More


How to Help Melancholicks: Mather

Jennifer Radden

in The Nature of Melancholy: From Aristotle to Kristeva

Published in print:
2002
Published Online:
October 2011
ISBN:
9780195151657
eISBN:
9780199849253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195151657.003.0012
Subject:
Philosophy, General

This chapter presents Cotton Mather's discussion of melancholy. Mather was a Puritan divine who lived between 1663 and 1728. Educated at Harvard, he was ordained in 1685 and later succeeded his ... More


Aubry-Mather type at the single resonance

Kaloshin Vadim and Zhang Ke

in Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter proves Aubry-Mather type in the single-resonance regime. It proves that for a single-resonance normal form system which satisfies the non-degeneracy conditions, every c in the resonance ... More


Miraculous Plagues: An Epidemiology of Early New England Narrative

Cristobal Silva

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199743476
eISBN:
9780199896868
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199743476.001.0001
Subject:
History, American History: early to 18th Century, Cultural History

This book reimagines New England’s literary history by tracing seventeenth- and early-eighteenth-century epidemics alongside the era of early colonial expansion, the Antinomian controversy, the ... More


Technologies of Inoculation

Cristobal Silva

in Miraculous Plagues: An Epidemiology of Early New England Narrative

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199743476
eISBN:
9780199896868
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199743476.003.0004
Subject:
History, American History: early to 18th Century, Cultural History

This chapter examines the interlinked histories of inoculation and print during the 1721 Boston inoculation controversy. Cotton Mather claimed that he learned about inoculation from his slave ... More


Abandoned and Adopted in a New World

Carol J. Singley

in Adopting America: Childhood, Kinship, and National Identity in Literature

Published in print:
2011
Published Online:
May 2011
ISBN:
9780199779390
eISBN:
9780199895106
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199779390.003.0001
Subject:
Literature, American, 19th Century Literature

The early Puritans ambivalently left England, the mother country, portraying themselves as abandoned orphans. Sustained by the belief that they were chosen people, they also emulated ... More


Managing Blackness: Protestant Readings of Psalm 68:31 in Colonial America

Roy Kay

in The Ethiopian Prophecy in Black American Letters

Published in print:
2011
Published Online:
January 2012
ISBN:
9780813037325
eISBN:
9780813041582
Item type:
chapter
Publisher:
University Press of Florida
DOI:
10.5744/florida/9780813037325.003.0003
Subject:
Literature, African-American Literature

This chapter demonstrates how three Anglophone Protestant writers, Fox, Sewall, and Mather employ Psalm 68:31 to situate Ethiopians in relation to white English colonialists and within God's ... More


For What America? Two Visions

Tracy B. Strong

in Learning One's Native Tongue: Citizenship, Contestation, and Conflict in America

Published in print:
2019
Published Online:
September 2020
ISBN:
9780226623191
eISBN:
9780226623368
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226623368.003.0002
Subject:
Political Science, American Politics

Early settlers thought the land given to them by God; Native Americans being a nuisance. It was in New England that they hoped to build a Godly perfected society. Two visions of this conflicted – ... More


The Puritan Cosmopolis: The Law of Nations and the Early American Imagination

Nan Goodman

Published in print:
2018
Published Online:
March 2018
ISBN:
9780190642822
eISBN:
9780190642846
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190642822.001.0001
Subject:
Literature, American, 18th Century and Early American Literature

This book traces the emergence of a sense of kinship with and belonging to a larger, more inclusive world within the law and literature of late seventeenth-century Puritanism. Connected to this ... More


Forcing Relation

Kaloshin Vadim and Zhang Ke

in Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter describes forcing relations, different diffusion mechanisms, and Aubry-Mather types. The Aubry set can be decomposed into disjoint invariant sets called static classes, which gives ... More


Double Resonance: Forcing Equivalence

Kaloshin Vadim and Zhang Ke

in Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Published in print:
2020
Published Online:
May 2021
ISBN:
9780691202525
eISBN:
9780691204932
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202525.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter assesses the choice of cohomology and Aubry-Mather type at the double resonance. It begins by choosing cohomology classes for the (unperturbed) slow mechanical system. As in the case of ... More


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