On analytic mappings among three-sheeted surfaces

Dynamical systems on infinitely sheeted Riemann surfaces

This paper is part of a program that aims to understand the connection between the emergence of chaotic behaviour in dynamical systems in relation with the multi-valuedness of the solutions as functions of complex time τ . In this work we consider a family of systems whose solutions can be expressed as the inversion of a single hyperelliptic integral. The associated Riemann surface R → C = {τ} ...

Analytic Mappings on Hyperfinite Sets

Let S and T be hyperfinite sets in an N]-saturated nonstandard universe. The following are equivalent: m 1*1 ~ l (l) rff ~ • • (ii) There is a bijection from 5 onto T whose graph is Borel (over the internal subsets of S x T). This follows from somewhat more general results about analytic partial functions on hyperfinite sets, the proofs of which use Choquet's theorem on the capacitibility of an...

Mappings On Decomposable Combinatorial Structures: Analytic Approach

Combinatorics, Probability & Computing / Volume 11 / Issue 01 / January 2002, pp 61 78 DOI: 10.1017/S0963548301005016, Published online: 14 February 2002 Link to this article: http://journals.cambridge.org/abstract_S0963548301005016 How to cite this article: E. MANSTAVICIUS (2002). Mappings on Decomposable Combinatorial Structures: Analytic Approach. Combinatorics, Probability & Computing, 11, ...

Complex Analytic Mappings

Analytic Behaviour of Competition among Three Species

We analyse the classical model of competition between three species studied by May and Leonard (SIAM J Appl Math 29 (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the parameters for which the system is integrable. We observe some striking relations between critical values arising from the approach of dynamical systems and the singularity ...