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Double Resonance: Geometric Description

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/9780691202525.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter examines the geometrical structure for the system at double resonance. After describing the normal form near a double resonance, it reduces the system to the slow mechanical system with ... More


Normally hyperbolic cylinders at double 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/9780691202525.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter proves the geometric picture of double resonance described in Chapter 4. There are two cases. In the simple critical homology case, the chapter shows the homoclinic orbit can be extended ... More


Index theorems for meromorphic self-maps of the projective space

Marco Abate

Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)

in Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159294
eISBN:
9781400851317
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159294.003.0017
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter uses techniques from the theory of local dynamics of holomorphic germs tangent to the identity to prove three index theorems for global meromorphic maps of projective space. More ... More


International University Consortia on the New Silk Road

Zhuolin Feng and Luyang Gao

in China and Europe on the New Silk Road: Connecting Universities Across Eurasia

Published in print:
2020
Published Online:
November 2020
ISBN:
9780198853022
eISBN:
9780191887420
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853022.003.0006
Subject:
Business and Management, Knowledge Management, Political Economy

International collaborations among higher education institutions have existed along the Silk Road for a long time. With the initiative of the Belt and Road, it is believed that cooperation among ... More


Time Measurement on the Ground in Kaga Domain

Yulia Frumer

in Making Time: Astronomical Time Measurement in Tokugawa Japan

Published in print:
2018
Published Online:
September 2018
ISBN:
9780226516448
eISBN:
9780226524719
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226524719.003.0007
Subject:
History, History of Science, Technology, and Medicine

Chapter 6 demonstrates how ideas about time measurement that originated in astronomical practice and spread in early nineteenth century Japanese society through surveying and navigation manifested in ... More


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