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Preface
A remark about Sil'nikov saddle-focus homoclinic orbits
1. | Dipartimento di Scienze Matematiche, Facoltà di Ingegneria, Università, Via Brecce Bianche, 1, 60100 Ancona |
2. | Department of Mathematics, National Taiwan University, Taipei 106 |
References:
[1] |
W.-J. Beyn, The numerical computation of connecting orbits in dynamical systems, IMA J. Numer. Anal., 10 (1990), 379-405.
doi: doi:10.1093/imanum/10.3.379. |
[2] |
W. A. Coppel, "Dichotomies in Stability Theory," Lecture Notes in Math., Vol. 629, Springer Verlag, Berlin, 1978. |
[3] |
B. Deng, On Sil'nikov's homoclinic-saddle-focus theorem, J. Diff. Equations, 102 (1993), 305-329.
doi: doi:10.1006/jdeq.1993.1031. |
[4] |
Y. A. Kuznetsov, "Elements of Applied Bifurcation Theory" 3rd Ed., Springer, 2004. |
[5] |
K. J. Palmer, Exponential dichotomies and transversal homoclinic points, J. Diff. Equations, 55 (1984), 225-256.
doi: doi:10.1016/0022-0396(84)90082-2. |
[6] |
J. A. Rodriguez, Bifurcation to homoclinic connections of the focus-saddle type, Arch. Rat. Mech. Anal., 93 (1986), 81-90.
doi: doi:10.1007/BF00250846. |
[7] |
B. Sandstede, Constructing dynamical systems having homoclinic bifurcation points of codimension two, J. Dynamics Diff. Eqns., 9 (1997), 269-288.
doi: doi:10.1007/BF02219223. |
[8] |
L. P. Sil'nikov, A case of the existence of a denumerable set of periodic motions, Soviet Math. Doklady, 6 (1965), 163-166. |
[9] |
L. P. Sil'nikov, A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type, Math. USSR Sbornik, 10 (1970), 91-102.
doi: doi:10.1070/SM1970v010n01ABEH001588. |
[10] |
L. P. Sil'nikov, A. L. Sil'nikov, D. V. Turaev and L. O. Chua, "Methods of Qualitative Theory in Nonlinear Dynamics," Part I, World Scientific, Singapore, 1998.
doi: doi:10.1142/9789812798596. |
[11] |
L. P. Sil'nikov, A. L. Sil'nikov, D. V. Turaev and L. O. Chua, "Methods of Qualitative Theory in Nonlinear Dynamics," Part II, World Scientific, Singapore, 2001.
doi: doi:10.1142/9789812798558. |
[12] |
S. R. Wiggins, "Global Bifurcations and Chaos: Analytical Methods," Applied Mathematical Sciences, 73, Springer-Verlag, New York, 1988. |
show all references
References:
[1] |
W.-J. Beyn, The numerical computation of connecting orbits in dynamical systems, IMA J. Numer. Anal., 10 (1990), 379-405.
doi: doi:10.1093/imanum/10.3.379. |
[2] |
W. A. Coppel, "Dichotomies in Stability Theory," Lecture Notes in Math., Vol. 629, Springer Verlag, Berlin, 1978. |
[3] |
B. Deng, On Sil'nikov's homoclinic-saddle-focus theorem, J. Diff. Equations, 102 (1993), 305-329.
doi: doi:10.1006/jdeq.1993.1031. |
[4] |
Y. A. Kuznetsov, "Elements of Applied Bifurcation Theory" 3rd Ed., Springer, 2004. |
[5] |
K. J. Palmer, Exponential dichotomies and transversal homoclinic points, J. Diff. Equations, 55 (1984), 225-256.
doi: doi:10.1016/0022-0396(84)90082-2. |
[6] |
J. A. Rodriguez, Bifurcation to homoclinic connections of the focus-saddle type, Arch. Rat. Mech. Anal., 93 (1986), 81-90.
doi: doi:10.1007/BF00250846. |
[7] |
B. Sandstede, Constructing dynamical systems having homoclinic bifurcation points of codimension two, J. Dynamics Diff. Eqns., 9 (1997), 269-288.
doi: doi:10.1007/BF02219223. |
[8] |
L. P. Sil'nikov, A case of the existence of a denumerable set of periodic motions, Soviet Math. Doklady, 6 (1965), 163-166. |
[9] |
L. P. Sil'nikov, A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type, Math. USSR Sbornik, 10 (1970), 91-102.
doi: doi:10.1070/SM1970v010n01ABEH001588. |
[10] |
L. P. Sil'nikov, A. L. Sil'nikov, D. V. Turaev and L. O. Chua, "Methods of Qualitative Theory in Nonlinear Dynamics," Part I, World Scientific, Singapore, 1998.
doi: doi:10.1142/9789812798596. |
[11] |
L. P. Sil'nikov, A. L. Sil'nikov, D. V. Turaev and L. O. Chua, "Methods of Qualitative Theory in Nonlinear Dynamics," Part II, World Scientific, Singapore, 2001.
doi: doi:10.1142/9789812798558. |
[12] |
S. R. Wiggins, "Global Bifurcations and Chaos: Analytical Methods," Applied Mathematical Sciences, 73, Springer-Verlag, New York, 1988. |
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