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2011, 2011(Special): 1289-1298. doi: 10.3934/proc.2011.2011.1289

Duck farming on the two-torus: Multiple canard cycles in generic slow-fast systems

Ilya Schurov 1,

1. 

Higher School of Economics — National Research University, Room 518, 3, Kochnovsky pr-d, Moscow, Russian Federation

Received  July 2010 Revised  April 2011 Published  October 2011

Generic slow-fast systems with only one (time-scaling) parameter on the two-torus have attracting canard cycles for arbitrary small values of this parameter. This is in drastic contrast with the planar case, where canards usually occur in two-parametric families. In present work, general case of nonconvex slow curve with several fold points is considered. The number of canard cycles in such systems can be effectively computed and is no more than the number of fold points. This estimate is sharp for every system from some explicitly constructed open set.
Keywords: canards, limit cycles, Poincaré map, Slow-fast systems, equation of variations.
Mathematics Subject Classification: Primary: 34E15, 37G15.
Citation: Ilya Schurov. Duck farming on the two-torus: Multiple canard cycles in generic slow-fast systems. Conference Publications, 2011, 2011 (Special) : 1289-1298. doi: 10.3934/proc.2011.2011.1289
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