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"Circle Map," which was written in 2012, takes inspiration from poems by Rumi, the thirteenth-century Persian mystic.
At the Armory, the Philharmonic capitalized on that painterly quality by creating a multimedia Saariaho experience, consisting of four pieces in unbroken succession: "Lumière et Pesanteur," or "Light and Gravity"; "d'om le vrai sens," or "Man's True Sense," a clarinet concerto; "Lonh," for voice and electronics; and "Circle Map," for orchestra and electronics.
The Finnish composer Kaija Saariaho, whose "L'Amour de Loin" will appear at the Met in December, receives a preparatory tribute from Esa-Pekka Salonen and the New York Philharmonic, which will offer "Circle Map," a surround-sound performance of four Saariaho pieces, at the Park Avenue Armory (Oct . 13-14.
A nonlinear circle map is suggested to model the dynamics of the modulator.
A key feature of an orbit of a degree-one circle map is its "rotation number".
An invariant set for a degree one circle map is called badly ordered if it contains three points in clockwise order whose images are not in clockwise order.
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Now we turn to discontinuous circle maps.
Consider continuous degree-one circle maps with a single decreasing interval.
This is in analogy to the formation of Arnold tongues in circle maps, for instance.
Underlying circle maps were extracted, and winding numbers were matched to response frequencies quantified in the fast Fourier transforms of the responses.
The nodal dynamics of the Bohr rotor is seen to have a quasi-fractal structure similar to that of earlier systems involving chaotic circle maps.
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