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Homoclinic Bifurcations in n Dimensions
Author(s) -
Fowler A. C.
Publication year - 1990
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1990833193
Subject(s) - homoclinic orbit , mathematics , eigenvalues and eigenvectors , aperiodic graph , quasiperiodic function , invariant (physics) , mathematical analysis , bernoulli's principle , bernoulli scheme , jacobian matrix and determinant , pure mathematics , periodic point , periodic orbits , mathematical physics , combinatorics , physics , bifurcation , quantum mechanics , nonlinear system , thermodynamics
Bifurcations near homoclinic orbits in n dimensions are described. Depending on the eigenvalues of the Jacobian at the fixed point whose real parts are closest to zero, a strange invariant set of periodic and aperiodic orbits can be produced, which can be described by a Bernoulli shift on a finite set of symbols. These results generalize earlier ones of Shil'nikov, Gaspard, Tresser, Glendinning, and Sparrow, amongst others.