ISSN:
1432-1467
Keywords:
break-up of heteroclinic connection
;
exponentially small splitting of separatrices
;
singular perturbation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Summary We consider a family ofq-dimensional (q〉1), volume-preserving maps depending on a small parameterε. Asε → 0+ these maps asymptote to flows which attain a heteroclinic connection. We show that for smallε the heteroclinic connection breaks up and that the splitting between its components scales withε likeε γexp[-β/ε]. We estimateβ using the singularities of theε → 0+ heteroclinic orbit in the complex plane. We then estimateγ using linearization about orbits in the complex plane. These estimates, as well as the assertions regarding the behavior of the functions in the complex plane, are supported by our numerical calculations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02429851
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