Exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant tori (Q1114977)
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scientific article; zbMATH DE number 4086595
| Language | Label | Description | Also known as |
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| English | Exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant tori |
scientific article; zbMATH DE number 4086595 |
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Exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant tori (English)
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1988
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An approximate renormalisation scheme is derived for the breakup of invariant tori of arbitrary winding ratio in Hamiltonian systems of one and a half degrees of freedom, similar to that of Escande and Doveil. It is a free semi-group with two generators. This scheme is solved exactly for its orbits, stable manifolds, unstable manifolds and critical set. Various results are found, including a Cantor set of universal fractal diagrams, the robustness of noble tori, and a scaling law for areas near critical circles.
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renormalisation scheme
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Hamiltonian systems
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free semi-group
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orbits
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stable manifolds
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unstable manifolds
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universal fractal diagrams
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