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Author: U Haagerup Publisher: ISBN: 9781470403737 Category : Hamiltonian systems Languages : en Pages : 162
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
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: Pierre Lochak Publisher: American Mathematical Soc. ISBN: 9780821864975 Category : Mathematics Languages : en Pages : 164
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: Pierre Lochak Publisher: American Mathematical Soc. ISBN: 0821832689 Category : Mathematics Languages : en Pages : 162
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: Joel Berman Publisher: American Mathematical Soc. ISBN: 0821837079 Category : Mathematics Languages : en Pages : 176
Book Description
Considers the behavior of $\mathrm{G}_\mathcal{C}(k)$ when $\mathcal{C}$ is a locally finite equational class (variety) of algebras and $k$ is finite. This title looks at ways that algebraic properties of $\mathcal{C}$ lead to upper or lower bounds on generative complexity.
Author: Trevor Alan Welsh Publisher: American Mathematical Soc. ISBN: 0821836560 Category : Mathematics Languages : en Pages : 176
Book Description
Fermionic expressions for all minimal model Virasoro characters $\chi DEGREES{p, p'}_{r, s}$ are stated and proved. Each such expression is a sum of terms of fundamental fermionic f
Author: Nicole Bopp Publisher: American Mathematical Soc. ISBN: 0821836234 Category : Mathematics Languages : en Pages : 250
Book Description
Intends to prove a functional equation for a local zeta function attached to the minimal spherical series for a class of real reductive symmetric spaces.
Author: Eva A. Gallardo-Gutieŕrez Publisher: American Mathematical Soc. ISBN: 0821834320 Category : Mathematics Languages : en Pages : 98
Book Description
Introduction and preliminaries Linear fractional maps with an interior fixed point Non elliptic automorphisms The parabolic non automorphism Supercyclic linear fractional composition operators Endnotes Bibliography.
Author: Arnd Scheel Publisher: American Mathematical Soc. ISBN: 0821833731 Category : Mathematics Languages : en Pages : 102
Book Description
Includes a paper that studies bifurcations of stationary and time-periodic solutions to reaction-diffusion systems. This title develops a center-manifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns.
Author: Helge Glöckner Publisher: American Mathematical Soc. ISBN: 0821832565 Category : Mathematics Languages : en Pages : 150
Book Description
A memoir that studies positive definite functions on convex subsets of finite- or infinite-dimensional vector spaces. It studies representations of convex cones by positive operators on Hilbert spaces. It also studies the interplay between positive definite functions and representations of convex cones.
Author: U Haagerup
Author: U Haagerup
Author: Pierre Lochak
Author: Pierre Lochak
Author: Joel Berman
Author: Trevor Alan Welsh
Author: 
Author: Nicole Bopp
Author: Eva A. Gallardo-Gutieŕrez
Author: Arnd Scheel
Author: Helge Glöckner