منابع مشابه
The Monodromy Groups of Schwarzian Equations on Closed Riemann Surfaces
Let θ : π1(R) → PSL(2,C) be a homomorphism of the fundamental group of an oriented, closed surface R of genus exceeding one. We will establish the following theorem. Theorem. Necessary and sufficient for θ to be the monodromy representation associated with a complex projective stucture on R, either unbranched or with a single branch point of order 2, is that θ(π1(R)) be nonelementary. A branch ...
متن کاملThe Monodromy Groups of Schwarzian Equations on Compact Riemann Surfaces
Let R be an oriented compact surface without boundary of genus exceeding one, and let θ : π1(R;O) → Γ ⊂ PSL(2,C) be a homomorphism of its fundamental group onto a nonelementary group Γ of Möbius transformations. We present a complete, self-contained proof of the following facts: (i) θ is induced by a complex projective structure for some complex structure on R if and only if θ lifts to a homomo...
متن کاملDichotomy results for delay differential equations with negative Schwarzian derivative
We gain further insight into the use of the Schwarzian derivative to obtain new results for a family of functional differential equations including the famous Wright’s equation and the Mackey-Glass type delay differential equations. We present some dichotomy results, which allow us to get easily computable bounds of the global attractor. We also discuss related conjectures, and formulate new op...
متن کاملWright Type Delay Differential Equations with Negative Schwarzian
We prove that the well-known 3/2 stability condition established for the Wright equation (WE) still holds if the nonlinearity p(exp(−x)−1) in WE is replaced by a decreasing or unimodal smooth function f with f (0) < 0 satisfying the standard negative feedback and below boundedness conditions and having everywhere negative Schwarz derivative.
متن کاملLorentzian Worldlines and Schwarzian Derivative
The aim of this note is to relate the classical Schwarzian derivative and the geometry of Lorentz surfaces of constant curvature. 1. The starting point of our investigations lies in the following remark (joint work with L. Guieu). Consider a curve y = f(x) in the Lorentz plane with metric g = dxdy. If f (x) > 0, then its Lorentz curvature can be computed : ̺(x) = f (x) (f (x)) and enjoys the qui...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2014
ISSN: 0022-0396
DOI: 10.1016/j.jde.2014.05.040