## 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

## Black Hole Spin

*Charles D. Bailyn*

### in What Does a Black Hole Look Like?

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691148823
- eISBN:
- 9781400850563
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691148823.003.0008
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter examines the spin of a black hole. The spin is usually described as a nondimensional parameter, which can range from zero (a nonspinning black hole) to one (a situation described as ... More

## The Geopolitical Orbits of Ancient India: The Geographical Frames of the Ancient Indian Dynasties

*Dilip K. Chakrabarti*

- Published in print:
- 2010
- Published Online:
- October 2012
- ISBN:
- 9780198069898
- eISBN:
- 9780199080052
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198069898.001.0001
- Subject:
- History, Ancient History / Archaeology

This book explores how the political history of ancient India has transpired in various geographical orbits, the definition of which has long bothered scholars. Contrary to widely held assumptions, ... More

## ORBIT COUNTING AND THE TUTTE POLYNOMIAL

*Peter J. Cameron*

### in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780198571278
- eISBN:
- 9780191718885
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198571278.003.0001
- Subject:
- Mathematics, Probability / Statistics

This chapter summarizes the various attempts to extend the Tutte polynomial of a matroid to a polynomial which counts orbits of a group on various sets of objects that the usual Tutte polynomial ... More

## From KAM Theory to Aubry-Mather 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/9780691164502.003.0002
- Subject:
- Mathematics, Applied Mathematics

This chapter discusses an illustrative example, namely the properties of invariant probability measures and orbits on KAM tori (or more generally, on invariant Lagrangian graphs). This will prepare ... More

## Action-Minimizing Curves for Tonelli Lagrangians

*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/9780691164502.003.0004
- Subject:
- Mathematics, Applied Mathematics

This chapter discusses the notion of action-minimizing orbits. In particular, it defines the other two families of invariant sets, the so-called Aubry and Mañé sets. It explains their main dynamical ... More

## Introduction

*Dilip K. Chakrabarti*

### in The Geopolitical Orbits of Ancient India: The Geographical Frames of the Ancient Indian Dynasties

- Published in print:
- 2010
- Published Online:
- October 2012
- ISBN:
- 9780198069898
- eISBN:
- 9780199080052
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198069898.003.0001
- Subject:
- History, Ancient History / Archaeology

The focal geographical points of the ancient Indian dynasties, together with the geographical orbits within which they tried to expand their political power and interacted with the other contemporary ... More

## The Potentials of World Communism: (August 1,1949)

*Herbert Marcuse*

### in Secret Reports on Nazi Germany: The Frankfurt School Contribution to the War Effort

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691134130
- eISBN:
- 9781400846467
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691134130.003.0032
- Subject:
- History, Military History

This chapter examines the potentials of international Communism, focusing on countries on the basis of their value as representatives of the different areas in which the ideology is now a significant ... More

## Functional integrals

*Helmut Hofmann*

### in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.003.0024
- Subject:
- Physics, Nuclear and Plasma Physics

This chapter presents a short review of path integrals in quantum mechanics. This is followed by a detailed discussion of the evaluation of the semi-classical propagator, involving quadratic ... More

## Independent particles and quasiparticles in finite nuclei

*Helmut Hofmann*

### in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.003.0003
- Subject:
- Physics, Nuclear and Plasma Physics

This chapter begins with an explanation of the application of Hartree-Fock for effective two-body forces. The benefits of exploiting those of Skyrme type are demonstrated and other interactions are ... More