ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Stankul G. V., Lichman V. A., Hadzhi P. I. Lyapunov exponents in the Henon–Heiles problem. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 1, pp. 71-74. DOI: 10.18500/0869-6632-2007-15-1-71-74

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Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2007-15-1-71-74

Lyapunov exponents in the Henon–Heiles problem

Autors: 
Stankul Grigorij Valerevich, Transnistrian State University named after Taras Shevchenko (PSU named after TG Shevchenko)
Lichman Vladimir Aleksandrovich, Transnistrian State University named after Taras Shevchenko (PSU named after TG Shevchenko)
Hadzhi Petr Ivanovich, Transnistrian State University named after Taras Shevchenko (PSU named after TG Shevchenko)
Abstract: 

By the way of combined integrating of the motion and variation equations we calculated the maximal characteristic Lyapunov exponents in the wide limits of energy and time for the Henon–Heiles problem. It follows from the fitting procedure that the best approximate function is the exponential one with the parameter values, which are different from the earlier obtained parameter values (Benettin et al.).

Key words: 
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Reference: 
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  3. Benettin G, Galgani L, Strelcyn JM. Kolmogorov entropy and numerical experiments. Phys. Rev. A. 1976;14:2338–2345. DOI: 10.1103/PhysRevA.14.2338.
  4. Shevchenko II. Phys. Lett. A. 1998;241:53–60.
  5. Shevchenko II, Mel'nikov AV. Lyapunov exponents in the Hénon-Heiles problem. JETP Letters. 2003;77(12):642–646.
  6. Wolf A, Swift J, Swinney HL, Vastano JA. Determining Lyapunov exponents from a time series. Physica D.: Nonlinear Phenomena. 1985;16:285–317. DOI: 10.1016/0167-2789(85)90011-9.
Received: 
06.07.2006
Accepted: 
03.10.2006
Published: 
28.02.2007
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