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Resonances for homoclinic trapped sets / Jean-Francois Bony...[et al.].

By: Contributor(s): Material type: TextTextSeries: Astérisque ; 405.Publication details: Paris : Societe Mathematique de France, 2018.Description: vii, 314 pages : illustrations ; 24 cmISBN:
  • 9782856298947
Subject(s): DDC classification:
  • 510=4 23 As853
Summary: We study semiclassical resonances generated by homoclinic trapped sets. First, under some general assumptions, we prove that there is no resonance in a region below the real axis. Then, we obtain a quantization rule and the asymptotic expansion of the resonances when there is a finite number of homoclinic trajectories. The same kind of results is proved for homoclinic sets of maximal dimension. Next, we generalize to the case of homoclinic/heteroclinic trajectories and we study the three bump case. In all these settings, the resonances may either accumulate on curves or form clouds. We also describe the corresponding resonant states.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510=4 As853 (Browse shelf(Opens below)) Checked out 08/11/2019 C26644
Total holds: 0

Includes bibliographical references.

We study semiclassical resonances generated by homoclinic trapped sets. First, under some general assumptions, we prove that there is no resonance in a region below the real axis. Then, we obtain a quantization rule and the asymptotic expansion of the resonances when there is a finite number of homoclinic trajectories. The same kind of results is proved for homoclinic sets of maximal dimension. Next, we generalize to the case of homoclinic/heteroclinic trajectories and we study the three bump case. In all these settings, the resonances may either accumulate on curves or form clouds. We also describe the corresponding resonant states.

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