Abstract
Using two and four dimensional symplectic maps as model problem we test a simple and fast method to separate chaotic from regular orbits and we compare with 3 other chaos indicators: the frequency, the sup-map and the Lyapunov characteristic exponent.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Celletti, A. and Froeschlé, C.: 1995, On the determination of the stochasticity threshold of invariant curves. Int. J. of Bifurcation and Chaos, 5, n.6.
Froeschlé, C.: 1970, A numerical study of the stochasticity of dynamical systems with two degrees of freedom. Astron. Astrophys.,9, 15–23.
Froeschlé, C.: 1971, On the number of isolating integrals in systems with three degrees of freedom. Astrophys. and Space Sciences, 14, 110.
Froeschlé, C.: 1972, Numerical study of a four-dimensional mapping. Astron. Astrophys., 16, 172.
Froeschlé, C. and Lega, E.: 1996, On the measure of the structure around the last KAM torus before and after its break-up. Celest. Mech. and Dynamical Astron., (in press).
Froeschlé, C. Lega, E., and Gonczi, R.: 1996, Fast Lyapunov indicators. Application to asteroidal motion. Celest. Mech. and Dynamical Astron., submitted.
Froeschlé, C. and Scheidecker, J.P.: 1973, Numerical study of a four dimensional mapping II. Astron. Astrophys., 22, 431–436.
Froeschlé, C. and Scheidecker, J.P.: 1973, On the disappearance of isolating integrals in systems with more than two degrees of freedom. Astrophys. and Space Sc., 25:373–386.
Laskar, J.: 1990, The chaotic motion of the solar system. A numerical estimate of the size of the chaotic zones. Icarus, 88, 266.
Laskar, J., Froeschlé, C., and Celletti, A.: 1992, The measure of chaos by the numerical analysis of the fundamental frequencies. Application to the standard mapping. Physica D, 56, 253.
Laskar, J. and Robutel, Ph.: 1993, The chaotic obliquity of the planets. Nature, 361, 608.
Lega, E. and Froeschlé, C.: 1996, Numerical investigations of the structure around an invariant KAM torus using the frequency map analysis. Physica D, 1345, 1.
Milani, A. and Nobili, A.: 1992, Nature, 357, 569.
Morbidelli, A. and Froeschlé, C.: 1996, On the relationship between Lyapunov times and macroscopic instability times. Celest. Mech. and Dynam. Astr., In press.
Morbidelli, A. and Giorgilli, A.: 1994, Superexponential stability of KAM tori. J. Stat. Phys., 78, 1607.
Morbidelli, A. and Guzzo, M.: 1996, The Nekhoroshev theorem and the asteroid belt dynamical system, published in this volume.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Lega, E., Froeschlé, C. (1997). Fast Lyapunov Indicators Comparison with other Chaos Indicators Application to Two and Four Dimensional Maps. In: Dvorak, R., Henrard, J. (eds) The Dynamical Behaviour of our Planetary System. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5510-6_18
Download citation
DOI: https://doi.org/10.1007/978-94-011-5510-6_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6320-3
Online ISBN: 978-94-011-5510-6
eBook Packages: Springer Book Archive