Jonathan Jaquette氏(Brandeis Univ.)講演会

高安 亮紀(筑波大学)
2020年 1月10日(金) 17:00-18:30
本文 Brandeis UniversityのJonathan Jaquette氏をお招きし、遅延微分方程式に関するJones' Conjectureの計算機援用証明の講演会を開催します。 是非ご参加ください。
講師 Jonathan Jaquette(Department of Mathematics, Brandeis University)
題目 A Computer Assisted Proof of Jones' Conjecture: Counting and Discounting Slowly Oscillating Periodic Solutions to Wright's Equation
アブストラクト A classical example of a nonlinear delay differential equations is Wright's equation: y'(t) = - α y(t - 1)[1 + y(t)], considering α > 0 and y(t) > -1. This talk discusses two conjectures associated with this equation: Wright's conjecture (1955), which states that the origin is the global attractor for all α ∈ (0, π/2]; and Jones' conjecture (1962), which states that there is a unique slowly oscillating periodic solution for α > π/2.
In this talk, I will discuss our computer assisted proofs of these conjectures. To prove Wright's conjecture our approach relies on a careful investigation of the neighborhood of the Hopf bifurcation occurring at α = π/2. Using a rigorous numerical integrator we characterize slowly oscillating periodic solutions and calculate their stability, proving Jones' conjecture for α ∈ [1.9, 6.0] and thereby all α ≥ 1.9. We complete the proof of Jones conjecture using global optimization methods, extended to treat infinite dimensional problems.


高安 亮紀