High degeneracy of effective Hamiltonian in two dimensions (Q2693063)
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scientific article; zbMATH DE number 7664872
| Language | Label | Description | Also known as |
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| English | High degeneracy of effective Hamiltonian in two dimensions |
scientific article; zbMATH DE number 7664872 |
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High degeneracy of effective Hamiltonian in two dimensions (English)
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17 March 2023
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Summary: Consider the effective Hamiltonian \(\overline{H}(p)\) associated with the mechanical Hamiltonian \(H(p,x)=\frac{1}{2}|p|^2+V(x)\). We prove that for generic \(V\), \(\overline{H}\) is piecewise one-dimensional in a dense open set in two dimensions using Aubry-Mather theory.
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homogenization
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effective Hamiltonian
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Aubry-Mather theory
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weak KAM theory
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