DOI: 10.1016/0167-2789(88)90032-2. Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry

Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry

10.1016/0167-2789(88)90032-2

Crossref journal-article

Elsevier BV

Physica D: Nonlinear Phenomena (78)

Bibliography

Armbruster, D., Guckenheimer, J., & Holmes, P. (1988). Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry. Physica D: Nonlinear Phenomena, 29(3), 257â282.

Authors 3

Dieter Armbruster (first)
John Guckenheimer (additional)
Philip Holmes (additional)

References 16 Referenced 204

10.1080/02681118608806011 / Dynamics and Stability of Systems / Steady-state mode interaction in the presence of O(2)-symmetry by Dangelmayr (1986)
10.1090/conm/056/855084 / Cont. Math. / Steady-state mode interaction in the presence of O(2)-symmetry and in non-flux boundary conditions by Dangelmayr (1986)
10.1090/conm/056/855089 / Cont. Math. / A codimension two bifurcation with circular symmetry by Guckenheimer (1986)
10.1098/rsta.1987.0050 / Phil. Trans. Roy. Soc. Lond. A / The Takens-Bogdanov bifurcation with O(2)-symmetry by Dangelmayr (1987)
{'key': '10.1016/0167-2789(88)90032-2_BIB5_1', 'first-page': '121', 'article-title': 'Strong spatial resonance and travelling waves in Benard convection', 'author': 'Jones', 'year': '1987', 'journal-title': 'Phys. Lett. A'} / Phys. Lett. A / Strong spatial resonance and travelling waves in Benard convection by Jones (1987)
10.1016/0375-9601(87)90008-9 / Phys. Lett. A / Strong spatial resonance and travelling waves in Benard convection by Jones (1987)
{'key': '10.1016/0167-2789(88)90032-2_BIB6', 'article-title': 'The interaction of two spatially resonant patterns in thermal convection I: Exact 1:2 resonance', 'author': 'Proctor', 'year': '1987', 'journal-title': 'J. Fluid Mech.'} / J. Fluid Mech. / The interaction of two spatially resonant patterns in thermal convection I: Exact 1:2 resonance by Proctor (1987)
{'key': '10.1016/0167-2789(88)90032-2_BIB7', 'series-title': 'The dynamics of coherent structures in the wall region of a turbulent boundary layer', 'author': 'Aubry', 'year': '1986'} / The dynamics of coherent structures in the wall region of a turbulent boundary layer by Aubry (1986)
{'key': '10.1016/0167-2789(88)90032-2_BIB8', 'series-title': 'Math. Proc. Camb. Phil. Soc.', 'article-title': 'Structurally stable heteroclinic cycles', 'author': 'Guckenheimer', 'year': '1987'} / Math. Proc. Camb. Phil. Soc. / Structurally stable heteroclinic cycles by Guckenheimer (1987)
{'key': '10.1016/0167-2789(88)90032-2_BIB9', 'series-title': 'Applications of Centre Manifold Theory', 'author': 'Carr', 'year': '1981'} / Applications of Centre Manifold Theory by Carr (1981)
{'key': '10.1016/0167-2789(88)90032-2_BIB10', 'series-title': 'Nonlinear oscillations, dynamical systems and bifurcations of vector fields', 'author': 'Guckenheimer', 'year': '1983'} / Nonlinear oscillations, dynamical systems and bifurcations of vector fields by Guckenheimer (1983)
{'key': '10.1016/0167-2789(88)90032-2_BIB11', 'series-title': 'Non-axisymmetric post-buckling behavior of a complete thin cylindrical shell under axial compression', 'author': 'Buzano', 'year': '1984'} / Non-axisymmetric post-buckling behavior of a complete thin cylindrical shell under axial compression by Buzano (1984)
10.1007/BF02416564 / Arch. Rat. Mech. Anal. / Dynamics and symmetry: Predictions for modulated waves in rotating fluids by Rand (1982)
{'key': '10.1016/0167-2789(88)90032-2_BIB13', 'series-title': 'Handbook of Mathematical Functions', 'author': 'Abramowitz', 'year': '1965'} / Handbook of Mathematical Functions by Abramowitz (1965)
{'key': '10.1016/0167-2789(88)90032-2_BIB14', 'series-title': 'Ordinary differential equations', 'author': 'Hale', 'year': '1969'} / Ordinary differential equations by Hale (1969)
{'key': '10.1016/0167-2789(88)90032-2_BIB15', 'first-page': '54', 'article-title': 'The existence of a denumerable set of periodic motions in four-dimensional space in an extended neighborhood of a saddle-focus', 'volume': '8', 'author': 'Silnikov', 'year': '1967', 'journal-title': 'Sov. Math. Doklady'} / Sov. Math. Doklady / The existence of a denumerable set of periodic motions in four-dimensional space in an extended neighborhood of a saddle-focus by Silnikov (1967)

Dates

Type	When
Created	22 years, 10 months ago (Oct. 17, 2002, 11:58 a.m.)
Deposited	6 years, 4 months ago (April 6, 2019, 12:57 p.m.)
Indexed	19 hours, 8 minutes ago (Sept. 3, 2025, 6 a.m.)
Issued	37 years, 8 months ago (Jan. 1, 1988)
Published	37 years, 8 months ago (Jan. 1, 1988)
Published Print	37 years, 8 months ago (Jan. 1, 1988)

Funders 0

None

BibTeX

@article{Armbruster_1988, title={Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry}, volume={29}, ISSN={0167-2789}, url={http://dx.doi.org/10.1016/0167-2789(88)90032-2}, DOI={10.1016/0167-2789(88)90032-2}, number={3}, journal={Physica D: Nonlinear Phenomena}, publisher={Elsevier BV}, author={Armbruster, Dieter and Guckenheimer, John and Holmes, Philip}, year={1988}, month=jan, pages={257–282} }

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