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SUMMARY:Kaname Matsue (Kyushu University\, Japan)
DTSTART:20210504T140000Z
DTEND:20210504T150000Z
DTSTAMP:20260423T024623Z
UID:CRM-CAMP/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRM-CAMP/39/
 ">Rigorous numerics of blow-up solutions for autonomous ODEs</a>\nby Kanam
 e Matsue (Kyushu University\, Japan) as part of CRM CAMP (Computer-Assiste
 d Mathematical Proofs) in Nonlinear Analysis\n\n\nAbstract\nHere I talk ab
 out the recent studies concerning rigorous numerics of blow-up solutions f
 or autonomous ODEs in a systematic way under a mild assumption of vector f
 ields. The fundamental tools used here are “compactifications” of pha
 se spaces which map the infinity to the boundary of transformed phase spa
 ces (the “horizon”)\, and “time-scale desingularizations determined 
 by the original vector fields”. Blow-up solutions are then essentially 
 transformed into solutions on stable manifolds of invariant sets on the ho
 rizon. In particular\, rigorous enclosures of blow-up solutions and their
  blow-up times can be validated by means of standard machineries of dynami
 cal systems such as ODE integrators\, locally defined Lyapunov functions a
 nd parameterization of invariant manifolds. Dynamical system approach sho
 wn here reveals many quantitative and qualitative nature of blow-up behavi
 or for various concrete dynamical systems. A series of works presented in
  the present talk (involving rigorous numerics) are based on joint works w
 ith Profs. Akitoshi Takayasu\, Nobito Yamamoto and Jean-Philippe Lessard.\
 n
LOCATION:https://researchseminars.org/talk/CRM-CAMP/39/
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