67:. However, measures in terms of 2-foldings and 10-foldings are sometimes found, since they correspond to the loss of one bit of information or one digit of precision respectively.
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of the system. By convention, it is defined as the time for the distance between nearby trajectories of the system to increase by a factor of
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78:. However, empirical estimation of the Lyapunov time is often associated with computational or inherent uncertainties.
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Friedland, G.; Metere, A. (2018). "Isomorphism between
Maximum Lyapunov Exponent and Shannon's Channel Capacity".
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While it is used in many applications of dynamical systems theory, it has been particularly used in
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Extracting
Knowledge from Time Series: An Introduction to Nonlinear Empirical Modeling
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Gerlach, E. (2009). "On the
Numerical Computability of Asteroidal Lyapunov Times".
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299:"A Comparison Between Methods to Compute Lyapunov Exponents"
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Bezruchko, Boris P.; Smirnov, Dmitry A. (5 September 2010).
45:. It is defined as the inverse of a system's largest
74:where it is important for the problem of the
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297:Tancredi, G.; Sánchez, A.; Roig, F. (2001).
188:1 cm of argon at triple point (84 K, 69 kPa)
57:The Lyapunov time mirrors the limits of the
264:Chaos, Scattering and Statistical Mechanics
27:is the characteristic timescale on which a
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266:, Cambridge University Press, 2005. p. 7
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16:Timescale of dynamical systems
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204:Belousov–Zhabotinsky reaction
157:Chemical chaotic oscillations
76:stability of the Solar System
239:. Springer. pp. 56–57.
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303:The Astronomical Journal
35:. It is named after the
168:chaotic oscillations
86:Typical values are:
315:2001AJ....121.1171T
180:at room temperature
72:celestial mechanics
214:Three-body problem
130:1–5 million years
43:Aleksandr Lyapunov
366:Dynamical systems
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106:20 million years
47:Lyapunov exponent
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309:(2): 1171–1179.
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209:Molecular chaos
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183:3.7Ă—10 seconds
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166:Hydrodynamic
160:5.4 minutes
146:Rotation of
141:4,000 years
112:Solar System
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137:36 Atalante
21:mathematics
283:1706.08638
220:References
171:2 seconds
122:Axial tilt
345:0901.4871
135:Orbit of
360:Category
198:See also
176:1 cm of
152:36 days
148:Hyperion
103:'s orbit
82:Examples
311:Bibcode
37:Russian
33:chaotic
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92:System
23:, the
340:arXiv
278:arXiv
178:argon
101:Pluto
241:ISBN
126:Mars
319:doi
307:121
124:of
53:Use
31:is
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64:e
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