Computable topological groups and Pontryagin duality

Melnikov, Alexander G.

doi:10.1090/tran/7355

Cited by 23 publications

(45 citation statements)

References 37 publications

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“…The system is assumed to lie initially in the unstable equilibrium state associated with the specific volume v = v 0 (the inflection point) and the temperature T = T 0 < T c . The small time-periodic fluctuation of the absolute temperature about T 0 has a form [20,21,[27][28][29]]…”

Section: Chaos In the Charged Dilaton-ads Black Hole Flow Under mentioning

confidence: 99%

“…The coefficients P T T (v 0 , T 0 ), P vT T (v 0 , T 0 ) and P T T T (v 0 , T 0 ) vanish because the pressure (12) is a linear function of the temperature T . The absence of P vv (v 0 , T 0 ) is attributed to a fact that the thermodynamics system (12) i.e., [20,21,[27][28][29] v…”

Section: Chaos In the Charged Dilaton-ads Black Hole Flow Under mentioning

confidence: 99%

“…Here, we set α = 0.01, b = 1, q = 1, T0 = 0.0313, and P0 = 0.0013. which could be regarded as a common feature of such kind of static AdS black holes. Supposing a spatially periodic thermal perturbation has a form[20,21,[27][28][29]…”

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confidence: 99%

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Thermal chaos of a charged dilaton-AdS black hole in the extended phase space

2020

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We have studied thermal chaotic behavior in the extended phase space for a charged dilaton-AdS black hole by Melnikov method and present the effect of dilaton parameter on the thermal chaos.Our result show that for the temporal perturbation the thermal chaos in the charged dilaton-AdS black hole occurs only if the perturbation amplitude is larger than certain a critical value, but for the spatially perturbation, the chaos always exists irrespective of perturbation amplitude.These behaviors are similar to those in other AdS black hole, which can be regarded as the common features of the static AdS black holes. Moreover, we also find that the critical temporal perturbation amplitude leading to chaos increases with the dilaton parameter and decreases with the charge. This means that under the temporal perturbation the presence of dilaton parameter makes the onset of chaos more difficult, which differs from that of the charge parameter.

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Section: Chaos In the Charged Dilaton-ads Black Hole Flow Under mentioning

confidence: 99%

Section: Chaos In the Charged Dilaton-ads Black Hole Flow Under mentioning

confidence: 99%

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Thermal chaos of a charged dilaton-AdS black hole in the extended phase space

2020

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“…Regarding Eq. (3), note that, in keeping with the assumption of the MM [24,25], it is assumed that one can write δ = εδ, where 0 < ε 1 while δ is of order unity. The term sn 2 (Ωt; m) sin x in Eq.…”

Section: A Order-chaos Thresholdmentioning

confidence: 99%

“…(1) with λ = 0). Analytical estimates of the chaotic threshold in parameter space are obtained by using Melnikov's method (MM) [24,25], while the phenomenon of OD is anticipated theoretically with the aid of an energy analysis. The interplay between heterogeneous connectivity and local decrease of the pulse's impulse in networks described by Eq.…”

Section: Introductionmentioning

confidence: 99%

Impulse-induced localized control of chaos in starlike networks

2016

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Locally decreasing the impulse transmitted by periodic pulses is shown to be a reliable method of taming chaos in starlike networks of dissipative nonlinear oscillators, leading to both synchronous periodic states and equilibria (oscillation death). Specifically, the paradigmatic model of damped kicked rotators is studied in which it is assumed that when the rotators are driven synchronously, i.e., all driving pulses transmit the same impulse, the networks display chaotic dynamics. It is found that the taming effect of decreasing the impulse transmitted by the pulses acting on particular nodes strongly depends on their number and degree of connectivity. A theoretical analysis is given explaining the basic physical mechanism as well as the main features of the chaos-control scenario.

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Computable Analysis and Classification Problems

Downey

Melnikov

2020

Lecture Notes in Computer Science

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Computable topological groups and Pontryagin duality

Cited by 23 publications

References 37 publications

Thermal chaos of a charged dilaton-AdS black hole in the extended phase space

Thermal chaos of a charged dilaton-AdS black hole in the extended phase space

Impulse-induced localized control of chaos in starlike networks

Computable Analysis and Classification Problems

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