Corpus ID: 115828179

Ordinary di?erential equations in the complex domain

  title={Ordinary di?erential equations in the complex domain},
  author={Einar Hille},
  • E. Hille
  • Published 1976
  • Physics, Mathematics
Modular Invariants and Generalized Halphen Systems
Generalized Halphen systems are solved in terms of functions that uniformize genus zero Riemann surfaces, with automorphism groups that are commensurable with the modular group. Rational mapsExpand
On analytic solutions of the heat equation with an operator coefficient
Let A be a bounded linear operator on a Banach space and let g a be vector-valued function that is analytic in a neighborhood of the origin of ℝ. We obtain conditions of the existence of analyticExpand
Transformations of Markov Processes and Classification Scheme for Solvable Driftless Diffusions
We propose a new classification scheme for diffusion processes for which the backward Kolmogorov equation is solvable in analytically closed form by reduction to hypergeometric equations of theExpand
Modular solutions to equations of generalized Halphen type
  • J. Harnad, J. McKay
  • Mathematics, Physics
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 2000
Solutions to a class of differential systems that generalize the Halphen system are determined in terms of automorphic functions whose groups are commensurable with the modular group. These functionsExpand
Semianalytical method for treatment of the N-body problem with complex total energy within the hyperharmonics approach
We develop the variable phase approach to analyze all the solutions of the N-body hyperradial equations. As a first result of this analysis, we display here how the usual cutoff of the long-rangeExpand
Computation of conformal maps by modified schwarz-christoffel transformations
In this thesis we explore four issues regarding the use of the Schwarz-Christoffel transformation and related methods as robust conformal mapping techniques. The first of these, the crowdingExpand
Slices of Parameter Space for Meromorphic Maps with Two Asymptotic Values
This paper is part of a program to understand the parameter spaces of dynamical systems generated by meromorphic functions with finitely many singular values. We give a full description of theExpand
Branch cuts of Stokes wave on deep water. Part II: Structure and location of branch points in infinite set of sheets of Riemann surface
uid surface of Stokes wave into the real line with uid domain mapped into the lower complex half-plane. There is one square root branch point per spatial period of Stokes located in the upper complexExpand
Decomposition of Levy trees along their diameter
We study the diameter of L{\'e}vy trees that are random compact metric spaces obtained as the scaling limits of Galton-Watson trees. L{\'e}vy trees have been introduced by Le Gall and Le Jan (1998)Expand
Dynamics of Some Rational Discrete Dynamical Systems via Invariants
This study includes complex Mobius transformations as well as the third-order Lyness recurrence in several discrete dynamical systems for which some invariants can be found. Expand