Rank One Chaos
نویسندگان
چکیده
منابع مشابه
Dissipative Homoclinic Loops and Rank One Chaos
We prove that when subjected to periodic forcing of the form pμ,ρ,ω(t) = μ(ρh(x, y) + sin(ωt)), certain second order systems of differential equations with dissipative homoclinic loops admit strange attractors with SRB measures for a set of forcing parameters (μ, ρ, ω) of positive measure. Our proof applies the recent theory of rank one maps, developed by Wang and Young [30, 34] based on the an...
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Let E be an optimal elliptic curve of conductor N , such that the L-function LE(s) of E vanishes to order one at s = 1. Let K be a quadratic imaginary field in which all the primes dividing N split. The Gross-Zagier theorem gives a formula that expresses the Birch and Swinnerton-Dyer conjectural order the Shafarevich-Tate group of E over K as a rational number. We extract an integer factor from...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2011
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.9380