By M. Aizenman (Chief Editor)

Articles during this volume:

1-35

Periodic Monopoles with Singularities and N=2 Super-QCD

Sergey A. Cherkis and Anton Kapustin

37-75

Heteroclinic Connections among Periodic Orbits in Planar limited round Three-Body challenge – a working laptop or computer Assisted Proof

Daniel Wilczak and Piotr Zgliczynski

77-100

Deformations of Vertex Algebras, Quantum Cohomology of Toric kinds, and Elliptic Genus

Fyodor Malikov and Vadim Schechtman

101-127

Equivariant ok -Theory, Generalized Symmetric items, and Twisted Heisenberg Algebra

Weiqiang Wang

129-183

A Magnetic version with a potential Chern-Simons part - (with an Appendix by means of F. Goodman and H. Wenzl)

Michael H. Freedman

185-190

Differentiation of SRB States: Correction and Complements

David Ruelle

191-227

Spectral research of Unitary Band Matrices

Olivier Bourget, James S. Howland and Alain Joye

229-251

Monstrous Branes

Ben Craps, Matthias R. Gaberdiel and Jeffrey A. Harvey

253-285

Birkhoff general shape for a few Nonlinear PDEs

Dario Bambusi

287-338

Distribution of the 1st Particle in Discrete Orthogonal Polynomial Ensembles

Alexei Borodin and Dmitriy Boyarchenko

339-358

Intersection Numbers of Twisted Cycles and the Correlation services of the Conformal box Theory

Katsuhisa Mimachi and Masaaki Yoshida

359-381

On the totally non-stop Spectrum of Stark Operators

Galina Perelman

383-422

Rigorous answer of the Gardner Problem

Mariya Shcherbina and Brunello Tirozzi

423-454

On the Gribov challenge for Generalized Connections

Christian Fleischhack

455-490

Cercignani's Conjecture is typically actual and continually nearly True

Cédric Villani

491-516

Asymptotics of Determinants of Bessel Operators

Estelle L. Basor and Torsten Ehrhardt

517-532

Spectral Estimates for Periodic Jacobi Matrices

Evgeni Korotyaev and Igor V. Krasovsky

533-555

Method of Quantum Characters in Equivariant Quantization

J. Donin and A. Mudrov

557-565

Supplement - at the constitution of desk bound options of the Navier-Stokes Equations

Peter Wittwer

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**Extra info for Communications in Mathematical Physics - Volume 234**

**Sample text**

Heteroclinic Connections Between Periodic Orbits in Three-Body Problem 47 Fig. 4. 5. Action of R on h-sets. 7) relates the maps and their inverses, hence beside mapping the support of N by R it will switch also the nominally stable and unstable directions. 11. Let N be a h-set. We define a h-set R(N ) as follows: • |R(N )| = R(|N |) • u(R(N )) = s(N ) and s(R(N)) = u(N ) • the homeomorphism cR(N) : Rn → Ru(R(N)) × Ru(S(N)) is given by cR(N) = cN T ◦ R −1 . Observe that according to the above definition we have R(N)− = R(N + ) = R(N T ,− ), R(N)+ = R(N − ) = R(N T ,+ ), R(t (c, u, s)) = t (R(c), R(s), R(u)).

In order to prove existence of a heteroclinic connection between L∗1 and L∗2 we need to find a chain of covering relations which starts close to L∗1 (begins with H12 ) and ends close to L∗2 (with H22 ). For this sake we choose the sets Ni along a numerically constructed (nonrigorous) heteroclinic orbit in the vicinity of the intersection of such an orbit with the section (see Fig. 9). 9 · 10−6 ), u0 u1 u2 u3 u4 u5 u6 u7 = = = = = = = = −R(s0 )/10, −R(s1 )/10, −R(s2 ), −R(s3 ), −R(s4 )/2, −R(s5 )/6, −R(s6 )/2, −R(s7 )/5.

A. Cherkis, A. Kapustin Similarly, if j− is the number of strictly negative i, then we have an identity m−j− +1 K = n+ − i. (76) i=m The curvature of Aˆ goes to zero as const/|r|3/2 for |r| → ∞, therefore Aˆ has well-defined limiting holonomies for r → ±∞. For r → +∞, n− of the eigenvalues of φˆ approach constant values z1 , z2 , . . , zn− , where zi is the z-coordinate of the i th singularity with ei = −1. The corresponding eigenvectors are also the eigenvectors of the limiting holonomy of Aˆ with eigenvalues eiχ1 , eiχ2 , .