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Resonances for Homoclinic Trapped Sets
 
Jean-François Bony IMB, CNRS, Université de Bordeaux, Talence, France
Setsuro Fujiié Ritsumeikan University, Kusatsu, Japan
Thierry Ramond Université Paris-Sud, CNRS, Orsay, France
Maher Zerzeri Université Paris 13, Sorbonne Paris Cité, CNRS, Villetaneuse, France
A publication of the Société Mathématique de France
Resonances for Homoclinic Trapped Sets
Softcover ISBN:  978-2-85629-894-7
Product Code:  AST/405
List Price: $90.00
AMS Member Price: $72.00
Please note AMS points can not be used for this product
Resonances for Homoclinic Trapped Sets
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Resonances for Homoclinic Trapped Sets
Jean-François Bony IMB, CNRS, Université de Bordeaux, Talence, France
Setsuro Fujiié Ritsumeikan University, Kusatsu, Japan
Thierry Ramond Université Paris-Sud, CNRS, Orsay, France
Maher Zerzeri Université Paris 13, Sorbonne Paris Cité, CNRS, Villetaneuse, France
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-894-7
Product Code:  AST/405
List Price: $90.00
AMS Member Price: $72.00
Please note AMS points can not be used for this product
  • Book Details
     
     
    Astérisque
    Volume: 405; 314 pp
    MSC: Primary 35; 37; 81

    The authors study semiclassical resonances generated by homoclinic trapped sets. First, under some general assumptions, they prove that there is no resonance in a region below the real axis. Then, they obtain a quantization rule and the asymptotic expansion of the resonances when there is a finite number of homoclinic trajectories. The same kind of result is proved for homoclinic sets of maximal dimension.

    Next, the authors generalize to the case of homoclinic/heteroclinic trajectories and study the three bump cases. In all of these settings, the resonances may either accumulate on curves or form clouds. The authors also describe the corresponding resonant states.

    A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

    Readership

    Graduate students and research mathematicians.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 405; 314 pp
MSC: Primary 35; 37; 81

The authors study semiclassical resonances generated by homoclinic trapped sets. First, under some general assumptions, they prove that there is no resonance in a region below the real axis. Then, they obtain a quantization rule and the asymptotic expansion of the resonances when there is a finite number of homoclinic trajectories. The same kind of result is proved for homoclinic sets of maximal dimension.

Next, the authors generalize to the case of homoclinic/heteroclinic trajectories and study the three bump cases. In all of these settings, the resonances may either accumulate on curves or form clouds. The authors also describe the corresponding resonant states.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.