Because the time of Lagrange and Euler, it's been popular that an realizing of algebraic curves can remove darkness from the image of inflexible our bodies supplied through classical mechanics. Many mathematicians have demonstrated a contemporary view of the function performed via algebraic geometry lately. This booklet provides a few of these smooth thoughts, which fall in the orbit of finite dimensional integrable structures. the most physique of the textual content offers a wealthy collection of equipment and ideas from algebraic geometry caused via classical mechanics, whereas in appendices the writer describes common, summary conception. She supplies the equipment a topological program, for the 1st time in ebook shape, to the examine of Liouville tori and their bifurcations.

Best Algebraic Geometry books

Fractured Fractals and Broken Dreams: Self-Similar Geometry through Metric and Measure (Oxford Lecture Series in Mathematics and Its Applications)

Fractal styles have emerged in lots of contexts, yet what precisely is a development? How can one make detailed the buildings mendacity inside items and the relationships among them? This e-book proposes new notions of coherent geometric constitution to supply a clean method of this normal box. It develops a brand new thought of self-similarity referred to as "BPI" or "big items of itself," which makes the sphere a lot more straightforward for individuals to go into.

The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

The idea of elliptic curves is unique by way of its lengthy background and through the range of the tools which were utilized in its learn. This publication treats the mathematics strategy in its sleek formula, by using simple algebraic quantity concept and algebraic geometry. Following a quick dialogue of the required algebro-geometric effects, the booklet proceeds with an exposition of the geometry and the formal workforce of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and international fields.

A First Course in Modular Forms (Graduate Texts in Mathematics, Vol. 228)

This booklet introduces the speculation of modular varieties, from which all rational elliptic curves come up, with an eye fixed towards the Modularity Theorem. dialogue covers elliptic curves as advanced tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner concept; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian kinds linked to Hecke eigenforms.

Additional info for Spinning Tops: A Course on Integrable Systems (Cambridge Studies in Advanced Mathematics)

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