Search results for "Chaotic dynamics"
showing 10 items of 197 documents
Universality for the breakup of invariant tori in Hamiltonian flows
1998
In this article, we describe a new renormalization-group scheme for analyzing the breakup of invariant tori for Hamiltonian systems with two degrees of freedom. The transformation, which acts on Hamiltonians that are quadratic in the action variables, combines a rescaling of phase space and a partial elimination of irrelevant (non-resonant) frequencies. It is implemented numerically for the case applying to golden invariant tori. We find a nontrivial fixed point and compute the corresponding scaling and critical indices. If one compares flows to maps in the canonical way, our results are consistent with existing data on the breakup of golden invariant circles for area-preserving maps.
Strange attractor for the renormalization flow for invariant tori of Hamiltonian systems with two generic frequencies
1999
We analyze the stability of invariant tori for Hamiltonian systems with two degrees of freedom by constructing a transformation that combines Kolmogorov-Arnold-Moser theory and renormalization-group techniques. This transformation is based on the continued fraction expansion of the frequency of the torus. We apply this transformation numerically for arbitrary frequencies that contain bounded entries in the continued fraction expansion. We give a global picture of renormalization flow for the stability of invariant tori, and we show that the properties of critical (and near critical) tori can be obtained by analyzing renormalization dynamics around a single hyperbolic strange attractor. We c…
Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity
2015
Abstract In this paper a Lorenz-like system, describing convective fluid motion in rotating cavity, is considered. It is shown numerically that this system, like the classical Lorenz system, possesses a homoclinic trajectory and a chaotic self-excited attractor. However, for the considered system, unlike the classical Lorenz system, along with self-excited attractor a hidden attractor can be localized. Analytical-numerical localization of hidden attractor is demonstrated.
Hidden Strange Nonchaotic Attractors
2021
In this paper, it is found numerically that the previously found hidden chaotic attractors of the Rabinovich–Fabrikant system actually present the characteristics of strange nonchaotic attractors. For a range of the bifurcation parameter, the hidden attractor is manifestly fractal with aperiodic dynamics, and even the finite-time largest Lyapunov exponent, a measure of trajectory separation with nearby initial conditions, is negative. To verify these characteristics numerically, the finite-time Lyapunov exponents, ‘0-1’ test, power spectra density, and recurrence plot are used. Beside the considered hidden strange nonchaotic attractor, a self-excited chaotic attractor and a quasiperiodic at…
Scenario of the Birth of Hidden Attractors in the Chua Circuit
2017
Recently it was shown that in the dynamical model of Chua circuit both the classical selfexcited and hidden chaotic attractors can be found. In this paper the dynamics of the Chua circuit is revisited. The scenario of the chaotic dynamics development and the birth of selfexcited and hidden attractors is studied. It is shown a pitchfork bifurcation in which a pair of symmetric attractors coexists and merges into one symmetric attractor through an attractormerging bifurcation and a splitting of a single attractor into two attractors. The scenario relating the subcritical Hopf bifurcation near equilibrium points and the birth of hidden attractors is discussed.
"2/NPART*VSInPbPb" of "Centrality and pseudorapidity dependence of the charged-particle multiplicity density in Xe-Xe collisions at $\sqrt{s_{\rm NN}…
2019
Values of $2/\langle N_\mathrm{part} \rangle \langle \mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\rangle$ and $2/\langle N_\mathrm{part} \rangle N^\mathrm{tot}_\mathrm{ch}$ as a function of $\langle N_\mathrm{part} \rangle$ in Pb--Pb collisions at $\sqrt{s_{_{\mathrm{NN}}}} = 5.02\,\mathrm{TeV}$.
"2/NPART*_VS_SCALEDInPbPb" of "Centrality and pseudorapidity dependence of the charged-particle multiplicity density in Xe-Xe collisions at $\sqrt{s_…
2019
Values of $2/\langle N_\mathrm{part} \rangle \langle \mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\rangle$ and $2/\langle N_\mathrm{part} \rangle N^\mathrm{tot}_\mathrm{ch}$ as a function of $(\langle N_\mathrm{part} \rangle -2)/(2A)$ in Pb--Pb collisions at $\sqrt{s_{_{\mathrm{NN}}}} = 5.02\,\mathrm{TeV}$.
"Table 4" of "$\Upsilon$ production and nuclear modification at forward rapidity in Pb-Pb collisions at $\mathbf{\sqrt{\textit{s}_{\textbf{NN}}}=5.02…
2021
Nuclear modification factor of $\Upsilon(1\mathrm{S})$ as a function of the average number of participants $\langle N_{\mathrm{part}} \rangle$ or as a function of the collision centrality.
"Table 5" of "$\Upsilon$ production and nuclear modification at forward rapidity in Pb-Pb collisions at $\mathbf{\sqrt{\textit{s}_{\textbf{NN}}}=5.02…
2021
Nuclear modification factor of $\Upsilon(2\mathrm{S})$ as a function of the average number of participants $\langle N_{\mathrm{part}} \rangle$ or as a function of the collision centrality.
Order and Chaos in the Statistical Mechanics of the Integrable Models in 1+1 Dimensions
1991
This paper was presented at the meeting under this title. But, originally, the more cumbersome ‘Quantum chaos — classical chaos in k-space: thermodynamic limits for the sine-Gordon models’ was proposed. Certainly this covers more technically the content of this paper.