Abstract
During the last few years much effort has been devoted to the study of temporal chaotic behavior of simple dynamical systems modeling turbulent-like phenomena in a great variety of macroscopic physical systems [1]. On the other hand the study of pattern formation occurring in extended systems has only recently become a very popular subject [2].
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References
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A homoclinic (heteroclinic) orbit is a solution which bi-asymptotically connects the same equilibrium solution (two different equilibrium solutions).
Two equilibrium solutions are equivalent if they belong to the same orbit of the discrete symmetry group which leaves the system invariant. In the cases considered here these are reflection symmetry and discrete translations. When two solutions are not equivalent in this sense, the defect connecting them is generally mobile and rather called a front.
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The terminology used comes from dynamical systems theory. One and a half degrees of freedom Hamiltonian systems are systems with one degree of freedom periodically driven by an external force.
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Coullet, P., Elphick, C., Repaux, D. (1987). Spatial Disorder in Extended Systems. In: Güttinger, W., Dangelmayr, G. (eds) The Physics of Structure Formation. Springer Series in Synergetics, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73001-6_23
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DOI: https://doi.org/10.1007/978-3-642-73001-6_23
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