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AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
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CONTENTS § 1. Introduction § 2. Unsolved problems. Conjectures. Generalizations § 3. The main ideas of the proof of the exponential estimate § 4. Steepness conditions. Precise statement of the main theorem § 5. Forbidden motions § 6. Resonances. Resonance zones and blocks § 7. Dependence of the diameters of the discs of fast drift on the steepness of the unperturbed Hamiltonian § 8. Condition for the non-overlapping of resonances § 9. Traps in frequency systems. Completion of the proof of the main theorem § 10. Statement of the lemma on the elimination of non-resonance harmonics, and of the technical lemmas used in the proof of the main theorem § 11. Remarks on the proof of the main theorem § 12. Application of the main theorem to the many-body problem References
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Citations
Cited by
Weinberg, S. (1989) · Annals of Physics · doi:10.1016/0003-4916(89)90276-5 · Cited by 494
Stochasticity in quantum systems
Zaslavsky, G. M. (1981) · Physics Reports · doi:10.1016/0370-1573(81)90127-7 · Cited by 364
Generalized time-energy uncertainty relations and bounds on lifetimes of resonances
Pfeifer, P., & Fröhlich, J. (1995) · Reviews of Modern Physics · doi:10.1103/revmodphys.67.759 · Cited by 141
Metadata
- Authors
- Nekhoroshev, N. N.
- Venue
- Russian Mathematical Surveys
- Publisher
- Steklov Mathematical Institute
- Published
- 1977-12-31
- Volume
- 32
- Issue
- 6
- Pages
- 1-65
- ISSN
- 0036-0279 (ISSN-L)
- 1468-4829
- OpenAlex
- W1966160012
- Cited by
- 760
- References
- 0
- FWCI
- 0.98
- Type
- journal article
- Language
- en
- Open access
- bronze
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- CoChat. (2026). Citation check: AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS. https://app.cochat.ai/papers/10.1070/rm1977v032n06abeh003859
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- Nekhoroshev, N. N. (1977). AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS. Russian Mathematical Surveys. https://doi.org/10.1070/rm1977v032n06abeh003859
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