Die Stabilit�tsfrage bei Differentialgleichungen

On stabilizing volatile product returns

“…The Lyapunov exponents therefore indicate parameter constellations where chaotic behavior can be expected. Following Perron (1930) however, a positive Lyapunov exponent of a second-order nonlinear difference equation (using its first-order approximation) is not a sufficient condition for an orbit to be chaotic. Leonov and Kuznetsov (2007) carry this argument to the context of a discrete dynamical systems.…”

Attractivity and Bifurcation for Nonautonomous Dynamical Systems

“…The classical concept of exponential dichotomy for nonautonomous linear differential equations has been established by PERRON [129,130] Given linear nonautonomous invariant manifolds M 1 , M 2 of (θ, ϕ), the sets…”

Hyperbolic Dynamical Systems

“…One considers bounded candidate constructs and an action on these by the map whose (unique) fixed point (parametrized by a point on the stable subspace) must be an orbit. Perron [Pn1,(13) p. 144], [Pn2,(10) p. 51], [Pn4,(30) p. 719] used a variant of Picard iteration (or variation of parameters) for solutions of differential and difference equations; Irwin [I] simplified this approach and combined it with the Banach Contraction Principle to obtain a short proof with strong conclusions [Ro4, Section 5.10], [We, LW, Yc].…”