Dynamical Systems Theory of Irreversibility

Gaspard, Pierre

doi:10.1007/1-4020-2947-0_6

Cited by 4 publications

(3 citation statements)

References 84 publications

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“…In particular, their entropy (the exponential of which in this case is related to the phase-space volume occupied by the ensamble of clones) increases with time (Gibbs 1902). Because of the exponential accumulation of errors in the presence of chaotic dynamics, the entropy increases in both forward and backward integrations (Gaspard 2005). Therefore, backward and forward integrations are statistically equivalent.…”

Section: The Fatal Flawsmentioning

confidence: 99%

No evidence for interstellar planetesimals trapped in the Solar system

Morbidelli

Batygin

Brasser

et al. 2020

Monthly Notices of the Royal Astronomical Society: Letters

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ABSTRACT In two recent papers published in MNRAS, Namouni and Morais claimed evidence for the interstellar origin of some small Solar system bodies, including: (i) objects in retrograde co-orbital motion with the giant planets and (ii) the highly inclined Centaurs. Here, we discuss the flaws of those papers that invalidate the authors’ conclusions. Numerical simulations backwards in time are not representative of the past evolution of real bodies. Instead, these simulations are only useful as a means to quantify the short dynamical lifetime of the considered bodies and the fast decay of their population. In light of this fast decay, if the observed bodies were the survivors of populations of objects captured from interstellar space in the early Solar system, these populations should have been implausibly large (e.g. about 10 times the current main asteroid belt population for the retrograde co-orbital of Jupiter). More likely, the observed objects are just transient members of a population that is maintained in quasi-steady state by a continuous flux of objects from some parent reservoir in the distant Solar system. We identify in the Halley-type comets and the Oort cloud the most likely sources of retrograde co-orbitals and highly inclined Centaurs.

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Section: The Fatal Flawsmentioning

confidence: 99%

No evidence for interstellar planetesimals trapped in the Solar system

Morbidelli

Batygin

Brasser

et al. 2020

Monthly Notices of the Royal Astronomical Society: Letters

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“…This linear relation thus could be a generic feature of periodically oscillatory perturbation in nonlinear dynamical systems (see the appendix for a rough analytical estimate on this), which will be investigated further in other nonlinear systems (e.g. Rössler [6,7] and Chen [8]) in future work. The generalization of time dependence of the control parameter including the mean part and oscillatory part will also be reported in a future publication [26], where an interesting question of the effect of resonance will be examined.…”

Section: Discussionmentioning

confidence: 95%

“…stem cell behaviour) [4]. Different systems used to simulate dynamical processes include those of Lorenz [5], Rössler [6,7] and Chen [8]. One of the interesting issues in these nonlinear systems is the effect of external perturbation on the dynamics, for instance, the possibility of controlling chaos by the application of small perturbation to a chaotic system to achieve a desirable behaviour [9,10].…”

Section: Introductionmentioning

confidence: 99%

Oscillatory control parameters in nonlinear chaotic systems

Mohamed

Kim

2013

Phys. Scr.

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For a better understanding of the role of control parameters in nonlinear dynamical systems, we examined numerically the effect of the oscillatory control parameter D = C0 cos(ω1t) on the Lorenz model for a dynamo, where C0 and ω1 are the driving amplitude and frequency, respectively. Despite the absence of the mean value of D, finite amplitude solutions are found for sufficiently large C0 and small ω1. Overall, smaller C0 and higher ω1 are less efficient in generating finite amplitude solutions, the bifurcation occurring at a larger value of C0 and a smaller value of ω1. Furthermore, we find a linear relationship between C0 and ω1 for the transition between finite amplitude and damping solutions.

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Nonequilibrium Nanosystems

Gaspard¹

2010

Nonlinear Dynamics of Nanosystems

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Dynamical Systems Theory of Irreversibility

Cited by 4 publications

References 84 publications

No evidence for interstellar planetesimals trapped in the Solar system

No evidence for interstellar planetesimals trapped in the Solar system

Oscillatory control parameters in nonlinear chaotic systems

Nonequilibrium Nanosystems

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