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Approach your problems from the It isn't that they can't see the
solution. right end and begin with the answers. It is that they
can't see the problem. Then one day, perhaps you will find the
final question. G. K. Chesterton. The Scandal of Father Brown 'The
point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van
Gulik's The Chinese Maze Murders. Growing specialization and
diversification have brought a host of monographs and textbooks on
increasingly specialized topics. However, the 'tree' of knowledge
of mathematics and related fields does not grow only by putting
forth new branches. It also happens, quite often in fact, that
branches which were thought to be completely disparate are suddenly
seen to be related. Further, the kind and level of sophistication
of mathematics applied in various sciences has changed drastically
in recent years: measure theory is used (non trivially) in regional
and theoretical economics; algebraic geometry interacts with
physics; the Minkowsky lemma, coding theory and the structure of
water meet one another in packing and covering theory; quantum
fields, crystal defects and mathematical programming profit from
homotopy theory; Lie algebras are relevant to filtering; and
prediction and electrical engineering can use Stein spaces. And in
addition to this there are such new emerging subdisciplines as
'experimental mathematics', 'CFD', 'completely integrable systems',
'chaos, synergetics and large-scale order', which are almost
impossible to fit into the existing classification schemes. They
draw upon widely different sections of mathematics."
This EMS volume, the first edition of which was published as
Dynamical Systems II, EMS 2, familiarizes the reader with the
fundamental ideas and results of modern ergodic theory and its
applications to dynamical systems and statistical mechanics. The
enlarged and revised second edition adds two new contributions on
ergodic theory of flows on homogeneous manifolds and on methods of
algebraic geometry in the theory of interval exchange
transformations.
This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The exposition starts from the basic of the subject, introducing ergodicity, mixing and entropy. The ergodic theory of smooth dynamical systems is treated. Numerous examples are presented carefully along with the ideas underlying the most important results. Moreover, the book deals with the dynamical systems of statistical mechanics, and with various kinetic equations. For this second enlarged and revised edition, published as Mathematical Physics I, EMS 100, two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations were added. This book is compulsory reading for all mathematicians working in this field, or wanting to learn about it.
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David Nicholls
Paperback
R395
R265
Discovery Miles 2 650
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