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Selected Chapters in the Calculus of Variations: Lecture Notes by Oliver Knill
(Lectures in Mathematics. ETH Zürich (closed)
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9783034880572 - Jurgen Moser: Selected Chapters in the Calculus of Variations
1
Jurgen Moser (?):

Selected Chapters in the Calculus of Variations (1982) (?)

ISBN: 9783034880572 (?) or 303488057X, probably in english, Birkhauser Basel, New, ebook, digital download

£ 55.17 ( 66.07)¹(free shipping, without obligation)
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Selected Chapters in the Calculus of Variations: 0.1 Introduction These lecture notes describe a new development in the calculus of variations which is called Aubry-Mather-Theory. The starting point for the theoretical physicist Aubry was a model for the descrip- tion of the motion of electrons in a two-dimensional crystal. Aubry investigated a related discrete variational problem and the corresponding minimal solutions. On the other hand, Mather started with a specific class of area-preserving annulus mappings, the so-called monotone twist maps. These maps appear in mechanics as Poincare maps. Such maps were studied by Birkhoff during the 1920s in several papers. In 1982, Mather succeeded to make essential progress in this field and to prove the existence of a class of closed invariant subsets which are now called Mather sets. His existence theorem is based again on a variational principle. Although these two investigations have different motivations, they are closely re- lated and have the same mathematical foundation. We will not follow those ap- proaches but will make a connection to classical results of Jacobi, Legendre, Weier- strass and others from the 19th century. Therefore in Chapter I, we will put together the results of the classical theory which are the most important for us. The notion of extremal fields will be most relevant. In Chapter II we will investigate variational problems on the 2-dimensional torus. We will look at the corresponding global minimals as well as at the relation be- tween minimals and extremal fields. In this way, we will be led to Mather sets. Englisch, Ebook
9783034880572 - Jürgen Moser: Selected Chapters in the Calculus of Variations
2
Jürgen Moser (?):

Selected Chapters in the Calculus of Variations (1982) (?)

Delivery from: Japan

ISBN: 9783034880572 (?) or 303488057X, probably in english, Springer Shop, New, ebook, digital download

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0.1 Introduction These lecture notes describe a new development in the calculus of variations which is called Aubry-Mather-Theory. The starting point for the theoretical physicist Aubry was a model for the descrip­ tion of the motion of electrons in a two-dimensional crystal. Aubry investigated a related discrete variational problem and the corresponding minimal solutions. On the other hand, Mather started with a specific class of area-preserving annulus mappings, the so-called monotone twist maps. These maps appear in mechanics as Poincare maps. Such maps were studied by Birkhoff during the 1920s in several papers. In 1982, Mather succeeded to make essential progress in this field and to prove the existence of a class of closed invariant subsets which are now called Mather sets. His existence theorem is based again on a variational principle. Although these two investigations have different motivations, they are closely re­ lated and have the same mathematical foundation. We will not follow those ap­ proaches but will make a connection to classical results of Jacobi, Legendre, Weier­ strass and others from the 19th century. Therefore in Chapter I, we will put together the results of the classical theory which are the most important for us. The notion of extremal fields will be most relevant. In Chapter II we will investigate variational problems on the 2-dimensional torus. We will look at the corresponding global minimals as well as at the relation be­ tween minimals and extremal fields. In this way, we will be led to Mather sets. eBook
9783034880572 - Jürgen Moser: Selected Chapters in the Calculus of Variations: Lecture Notes by Oliver Knill (Lectures in Mathematics. ETH Zürich (closed))
3
Jürgen Moser (?):

Selected Chapters in the Calculus of Variations: Lecture Notes by Oliver Knill (Lectures in Mathematics. ETH Zürich (closed)) (2003) (?)

ISBN: 9783034880572 (?) or 303488057X, in english, 140 pages, Birkhäuser, New, first edition, ebook, digital download

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These lecture notes describe the Aubry-Mather-Theory within the calculus of variations. The text consists of the translated original lectures of Jürgen Moser and a bibliographic appendix with comments on the current state of the art in this field of interest. Students will find a rapid introduction to the calculus of variations, leading to modern dynamical systems theory. Differential geometric applications are discussed, in particular billiards and minimal geodesics on the two-dimensional torus. Many exercises and open questions make this book a valuable resource for both teaching and research. Kindle Edition, Ausgabe: 1, Format: Kindle eBook, Label: Birkhäuser, Birkhäuser, Produktgruppe: eBooks, Publiziert: 2003-08-05, Freigegeben: 2003-04-30, Studio: Birkhäuser
9783034880572 - Jürgen Moser: Selected Chapters in the Calculus of Variations
4
Jürgen Moser (?):

Selected Chapters in the Calculus of Variations (?)

ISBN: 9783034880572 (?) or 303488057X, in german, Birkhäuser, New, ebook

£ 22.57 ($ 29.99)¹(without obligation)
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Calculus of Variations and Optimal Control; Optimization, These lecture notes describe the Aubry-Mather-Theory within the calculus of variations. The text consists of the translated original lectures of Jürgen Moser and a bibliographic appendix with comments on the current state of the art in this field of interest. Students will find a rapid introduction to the calculus of variations, leading to modern dynamical systems theory. Differential geometric applications are discussed, in particular billiards and minimal geodesics on the two-dimensional torus. Many exercises and open questions make this book a valuable resource for both teaching and research.
9783034880572 - Jürgen Moser: Selected Chapters in the Calculus of Variations
5
Jürgen Moser (?):

Selected Chapters in the Calculus of Variations (?)

ISBN: 9783034880572 (?) or 303488057X, in german, Springer Nature, New, ebook

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Calculus of Variations, Extremal fields, Global minimals, Minimal geodesics, Twist maps, Variational problems, calculus, compactness, differential equation, extrema, minimum, theorem, Mathematics; Calculus of Variations and Optimal Control; Optimization; Differential Geometry, eBook
9783034880572 - Volker Schulze: Selected Chapters in the Calculus of Variations
6
Volker Schulze (?):

Selected Chapters in the Calculus of Variations (?)

ISBN: 9783034880572 (?) or 303488057X, in english, Wiley, New, ebook, digital download

£ 27.19 + Shipping: £ 9.99 = £ 37.18(without obligation)
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