Download Global analysis of dynamical systems: festschrift dedicated by H.W Broer, B Krauskopf, Gert Vegter PDF

By H.W Broer, B Krauskopf, Gert Vegter

Contributed by way of shut colleagues, pals, and previous scholars of Floris Takens, worldwide research of Dynamical structures is a liber amicorum devoted to Takens for his sixtieth birthday. the 1st bankruptcy is a replica of Takens's 1974 paper "Forced oscillators and bifurcations" that used to be formerly on hand basically as a preprint of the college of Utrecht. between different very important effects, it includes the unfolding of what's referred to now because the Bogdanov-Takens bifurcation. the rest chapters hide subject matters as varied as bifurcation thought, Hamiltonian mechanics, homoclinic bifurcations, routes to chaos, ergodic idea, renormalization concept, and time sequence research. In its entirety, the booklet bears witness to the impression of Takens at the smooth idea of dynamical structures and its purposes. This ebook is a must-read for somebody drawn to this energetic and intriguing box.

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Additional info for Global analysis of dynamical systems: festschrift dedicated to Floris Takens for his 60th birthday

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If the clocks do not interact, the coupling strength is zero. If the beam is not rigid, but can vibrate longitudinally or bend, then an interaction takes place. 2. Frequency detuning Frequency detuning or mismatch f = f 1 − f 2 quantifies how different the uncoupled oscillators are. In contrast to the coupling strength, in experiments with clocks detuning can be easily measured and varied. 1). 3 Mechanical clocks usually have a mechanism that easily allows one to do this. The process is used to force the clock to go faster if it is behind the exact time, and to force it to slow down if it is ahead.

2 that all trajectories tend to the cycle. 4 The reason why we distinguish this curve from all others is thus that it attracts phase trajectories5 and is therefore called an attractor of the dynamical system. 6 To conclude, self-sustained oscillations can be described by their image in the phase space – by the limit cycle. The form of the cycle, and, hence, the form of oscillation is entirely determined by the internal parameters of the system. If this oscillation is close in form to a sine wave, then the oscillator is called quasilinear (quasiharmonic).

Introduction 14 of the phases4 of two clocks. This helps us to distinguish between two different synchronous regimes. If two pendula move in the same direction and almost simultaneously attain, say, the rightmost position, then their phases φ1 and φ2 are close and this state is called in-phase synchronization (Fig. 10a). If we look at the motions of pendula precisely (we would probably need rather complicated equipment in order to do this), we can detect that the motions are not exactly simultaneous.

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