Author: Pierre Lochak
Publisher: American Mathematical Soc.
ISBN: 0821832689
Category : Mathematics
Languages : en
Pages : 162
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Book Description
Presents the problem of the splitting of invariant manifolds in multidimensional Hamiltonian systems, stressing the canonical features of the problem. This book offers introduction of a canonically invariant scheme for the computation of the splitting matrix.
Author: U Haagerup
Publisher:
ISBN: 9781470403737
Category : Hamiltonian systems
Languages : en
Pages : 162
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Book Description
Presents the problem of the splitting of invariant manifolds in multidimensional Hamiltonian systems, stressing the canonical features of the problem. This book offers introduction of a canonically invariant scheme for the computation of the splitting matrix.
Author:
Publisher: American Mathematical Soc.
ISBN: 0821834452
Category :
Languages : en
Pages : 102
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Book Description
Author: Pierre Lochak
Publisher: American Mathematical Soc.
ISBN: 9780821864975
Category : Mathematics
Languages : en
Pages : 164
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Book Description
In this text we take up the problem of the splitting of invariant manifolds in multidimensional Hamiltonian systems, stressing the canonical features of the problem. We first conduct a geometric study, which for a large part is not restricted to the perturbative situation of near-integrable systems. This point of view allows us to clarify some previously obscure points, in particular the symmetry and variance properties of the splitting matrix (indeed its very definition(s)) and more generally the connection with symplectic geometry. Using symplectic normal forms, we then derive local exponential upper bounds for the splitting matrix in the perturbative analytic case, under fairly general circumstances covering in particular resonances of any multiplicity. The next technical input is the introduction of a canonically invariant scheme for the computation of the splitting matrix. It is based on the familiar Hamilton-Jacobi picture and thus again is symplectically invariant from the outset. It is applied here to a standard Hamiltonian exhibiting many of the important features of the problem and allows us to explore in a unified way the question of finding lower bounds for the splitting matrix, in particular that of justifying a first order computation (the so-called Poincare-Melnikov approximation). Although we do not specifically address the issue in this paper we mention that the problem of the splitting of the invariant manifold is well-known to be connected with the existence of a global instability in these multidimensional Hamiltonian systems and we hope the present study will ultimately help shed light on this important connection first noted and explored by V. I. Arnold.
Author: Rajendra Bhatia
Publisher: World Scientific
ISBN: 9814462934
Category : Mathematics
Languages : en
Pages : 4137
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Book Description
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 0821837168
Category : Mathematics
Languages : en
Pages : 134
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Book Description
Introduction Partial commutative monoids Continuous dimension scales Espaliers Classes of espaliers Bibliography Index
Author: Valentin Poenaru
Publisher: American Mathematical Soc.
ISBN: 0821834606
Category : Mathematics
Languages : en
Pages : 104
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Book Description
Shows that at the cost of replacing $V DEGREES3$ by $V_h DEGREES3 = \{V DEGREES3$ with very many holes $\}$, we can always find representations $X DEGREES2 \stackrel {f} {\rightarrow} V DEGREES3$ with $X DEGREES2$ locally finite and almost-arborescent, with $\Psi (f)=\Phi (f)$, and with the ope
Author: Stefano Pigola
Publisher: American Mathematical Soc.
ISBN: 0821836390
Category : Mathematics
Languages : en
Pages : 118
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Book Description
Aims to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity obtained by the authors.
Author: Yaozhong Hu
Publisher: American Mathematical Soc.
ISBN: 0821837044
Category : Mathematics
Languages : en
Pages : 144
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Book Description
A paper that studies two types of integral transformation associated with fractional Brownian motion. They are applied to construct approximation schemes for fractional Brownian motion by polygonal approximation of standard Brownian motion. This approximation is the best in the sense that it minimizes the mean square error.
Author: Martin W. Liebeck
Publisher: American Mathematical Soc.
ISBN: 0821834827
Category : Mathematics
Languages : en
Pages : 242
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Book Description
Intends to complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This title follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small.
