Uniformly Hyperbolic Attractor of the Smale-Williams Type for a Poincaré Map in the Kuznetsov System

Hyperbolic systems of dissipative type, contracting the phase space volume, manifest robust attractors. There are several classes of discrete time systems which produce hyperbolic nontrivial attractor – like the Plykin attractors [P] or the Smale attractors [KH]. Recently, Kuznetsov [K] proposed a continuous model for which there is a good numerical evidence of the existence of an uniformly hyperbolic attractor. This is a non-autonomous system in R and it is constructed on a basis of two coupled van der Pol oscillators:  ẋ = ω0u u̇ = −ω0x+ ( A cos(2πt/T ) − x ) u+ (ε/ω0)y cos(ω0t) ẏ = 2ω0v v̇ = −2ω0y + ( −A cos(2πt/T ) − y ) v + (ε/2ω0)x 2