Chaotic and Fractal Dynamics: Introduction for Applied Scientists and Engineers
A revision of a professional text on the phenomena of chaotic vibrations in fluids and solids. Major changes reflect the latest developments in this fast-moving topic, the introduction of problems to every chapter, additional mathematics and applications, more coverage of fractals, numerous computer and physical experiments. Contains eight pages of 4-color pictures.
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amplitude basin boundary bifurcation buckled beam calculate chaos chaotic dynamics chaotic motions chaotic vibrations Chapter circle map circuit classical complex control parameter convection coupled criterion curve damping deﬁne deﬁnition difference equations differential equations discussed Dufﬁng dynamical system equilibrium points example experimental experiments Feigenbaum ﬁnd ﬁnite ﬁrst ﬁrst-order ﬁxed points ﬂow ﬂuid Fourier fractal dimension frequency function Henon map Holmes homoclinic orbit horseshoe map inﬁnite initial conditions iterations limit cycle linear logistic map Lyapunov exponent magnetic ﬁeld mass mathematical measure mechanical Moon nondimensional nonlinear dynamics one-dimensional map particle patterns pendulum period doubling periodic motion periodically forced phase plane phase space phenomena physical systems Poincaré map Poincaré section problem quasiperiodic motion regions rotation saddle point set of points shown in Figure signal Sketch solutions spatial spectrum stable strange attractor subharmonic theory three-dimensional tion trajectories two-well potential unstable manifolds variable velocity versus xn+l