Cuadro de texto: Distinguished hyperbolic trajectories (Mancho, Small, Wiggins, Ide, 2003; Mancho, Small, Wiggins, 2004; 2006) Cuadro de texto: This methodology distinguishes hyperbolic points which are ‘more fixed than their neiborhood’ The analogous to fixed points in time-independent flows or to periodic orbits in periodic flows. Cuadro de texto: dx/dt=v(x) Cuadro de texto: Tentative trajectory x0(t) Cuadro de texto: Expand around it: x(t)= x0(t)+d(t) Cuadro de texto: dd/dt = Dv(x0(t)) d + NL(d,t) Cuadro de texto: General solution: d(t) = sum of exponentials + Integral(exp … NL(d,t)) Cuadro de texto: Choosing initial conditions such that dh(t)=0 garantees a distinguished solution x(t)= x0(t)+d(t) which is not wandering arround exponentially fast, and neighbouring trajectories approach or escape from it exponentially Cuadro de texto: dp(t) Cuadro de texto: dh(t)

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