Unconditional Proof of the Boltzmann-Sinai Ergodic Hypothesis
We consider the system of \(N\) (\(\ge2\)) elastically colliding hard balls of masses \(m_1,...,m_N\) and radius \(r\) on the flat unit torus \(\Bbb T^\nu\), \(\nu\ge2\). We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the full hyperbolicity and ergodicity of such systems for every...
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| description | We consider the system of \(N\) (\(\ge2\)) elastically colliding hard balls of masses \(m_1,...,m_N\) and radius \(r\) on the flat unit torus \(\Bbb T^\nu\), \(\nu\ge2\). We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the full hyperbolicity and ergodicity of such systems for every selection \((m_1,...,m_N;r)\) of the external geometric parameters. The present proof does not use the formerly developed, rather involved algebraic techniques, instead it employs exclusively dynamical methods and tools from geometric analysis. |
| doi_str_mv | 10.48550/arxiv.0803.3112 |
| format | Article |
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| subjects | Ergodic processes Hypotheses Mathematical analysis Mathematics - Dynamical Systems Toruses |
| title | Unconditional Proof of the Boltzmann-Sinai Ergodic Hypothesis |
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