منابع مشابه
COUNTING TROPICAL ELLIPTIC PLANE CURVES WITH FIXED j-INVARIANT
In complex algebraic geometry, the problem of enumerating plane elliptic curves of given degree with fixed complex structure has been solved by R.Pandharipande [8] using Gromov-Witten theory. In this article we treat the tropical analogue of this problem, the determination of the number Etrop(d) of tropical elliptic plane curves of degree d and fixed “tropical j-invariant” interpolating an appr...
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A study of rational maps of the real or complex projective plane of degree two or more, concentrating on those which map an elliptic curve onto itself, necessarily by an expanding map. We describe relatively simple examples with a rich variety of exotic dynamical behaviors which are perhaps familar to the applied dynamics community but not to specialists in several complex variables. For exampl...
متن کاملElliptic Curves as Attractors in ℙ2 Part 1: Dynamics
A study of rational maps of the real or complex projective plane of degree two or more, concentrating on those which map a genus one curve onto itself, necessarily by an expanding map. We describe relatively simple examples with a rich variety of interesting dynamical behaviors which are perhaps familiar to the applied dynamics community but not to specialists in several complex variables. For ...
متن کاملAsymptotes, Cubic Curves, and the Projective Plane
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متن کاملFrom Invariant Curves to Strange Attractors
We prove that simple mechanical systems, when subjected to external periodic forcing, can exhibit a surprisingly rich array of dynamical behaviors as parameters are varied. In particular, the existence of global strange attractors with fully stochastic properties is proved for a class of second order ODEs.
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 2009
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-009-9104-9