Attractors of Quasiperiodically Forced Systems
This book discusses the influence of quasiperiodic force on dynamical system. With this type of forcing, different types of attractors are possible, for example, strange nonchaotic attractors which have some unusual properties.The main part of this book is based on the authors' recent works, but it also presents the results which are the combined achievements of many investigators.
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calculations Cantor set capacity dimension Chaos chaotic behaviour chaotic transients characteristic collision consider constant control parameter correlation dimension curve defined describe differential equation dissipative system dry friction dynamical systems embedding dimension equation 3.1 equilibrium example experimental finite frequency torus friction force Hopf bifurcation horizontal advection horseshoe map information dimension initial conditions Kapitaniak Lett limit cycle linearized equation Lyapunov dimension matrix maximum Lyapunov exponent nearby trajectories negative Nino noisy periodicity nonlinear systems observe obtained ocean Peano Peano curve Peano-Hilbert periodic forcing phase space Phys plot positive Lyapunov exponent power spectra predictability properties quasiperiodic behaviour quasiperiodic function quasiperiodic solution quasiperiodically forced systems relative velocity represents Saltzman sensitive dependence shown in Figure simple small orbit strange attractors strange chaotic attractor strange nonchaotic attractors strange nonchaotic behaviour strange nonchaotic transients surface temperature transient Lyapunov exponent transient strange nonchaotic two-dimensional type of attractor typical variables Volume winding number