Computer-assisted techniques for the verication of the Chebyshev property of Abelian integrals

Series: 
CDSNS Colloquium
Thursday, August 22, 2013 - 14:00
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
Uppsala Univ.
Organizer: 
Abstract: We develop techniques for the verication of the Chebyshev property of Abelian integrals. These techniques are a combination of theoretical results, analysis of asymptotic behavior of Wronskians, and rigorous computations based on interval arithmetic. We apply this approach to tackle a conjecture formulated by Dumortier and Roussarie in [Birth of canard cycles, Discrete Contin. Dyn. Syst. 2 (2009), 723781], which we are able to prove for q <= 2.