Examinando por Autor "Nieto, Alexandre R."

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A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering
(Springer, 2022) Nieto, Alexandre R.; Seoane, Jesús M.; Barrio, Roberto; Sanjuán, Miguel A. F.
Abstract In the context of nonhyperbolic chaotic scattering, it has been shown that the evolution of the KAM islands exhibits four abrupt metamorphoses that strongly affect the predictability of Hamiltonian systems. It has been suggested that these metamorphoses are related to significant changes in the structure of the KAM islands. However, previous research has not provided an explanation of the mechanisms underlying the metamorphoses. Here, we show that they occur due to the formation of a homoclinic or heteroclinic tangle that breaks the internal structure of the main KAM island. We obtain similar qualitative results in a two-dimensional Hamiltonian system and a twodimensional area-preserving map. The equivalence of the results obtained in both systems suggests that the same four metamorphoses play an important role in conservative systems.
Control of escapes in two-degree-of-freedom open Hamiltonian systems
(American Institute of Physics (AIP), 2022) Nieto, Alexandre R.; Lilienkamp, Thomas; Seoane, Jesús M.; Sanjuán, Miguel A.F.; Parlitz, Ulrich
We investigate the possibility of avoiding the escape of chaotic scattering trajectories in two-degree-of-freedom Hamiltonian systems. We develop a continuous control technique based on the introduction of coupling forces between the chaotic trajectories and some periodic orbits of the system. The main results are shown through numerical simulations, which confirm that all trajectories starting near the stable manifold of the chaotic saddle can be controlled. We also show that it is possible to jump between different unstable periodic orbits until reaching a stable periodic orbit belonging to a Kolmogorov–Arnold–Moser island.
Energy-based stochastic resetting can avoid noise-enhanced stability
(American Physical Society (APS), 2024) Cantisán, Julia; Nieto, Alexandre R.; Seoane, Jesús M.; Sanjuán, Miguel A.F.
The theory of stochastic resetting asserts that restarting a stochastic process can expedite its completion. In this paper, we study the escape process of a Brownian particle in an open Hamiltonian system that suffers noise-enhanced stability. This phenomenon implies that under specific noise amplitudes the escape process is delayed. Here, we propose a protocol for stochastic resetting that can avoid the noise-enhanced stability effect. In our approach, instead of resetting the trajectories at certain time intervals, a trajectory is reset when a predefined energy threshold is reached. The trajectories that delay the escape process are the ones that lower their energy due to the stochastic fluctuations. Our resetting approach leverages this fact and avoids long transients by resetting trajectories before they reach low-energy levels. Finally, we show that the chaotic dynamics (i.e., the sensitive dependence on initial conditions) catalyzes the effectiveness of the resetting strategy.
Final state sensitivity in noisy chaotic scattering
(Elsevier, 2021) Nieto, Alexandre R.; Seoane, Jesús M; Sanjuán, Miguel A.F.
The unpredictability in chaotic scattering problems is a fundamental topic in physics that has been studied either in purely conservative systems or in the presence of weak perturbations. In many systems noise plays an important role in the dynamical behavior and it models their internal irregularities or their coupling with the environment. In these situations the unpredictability is affected by both the chaotic dynamics and the stochastic fluctuations. In the presence of noise two trajectories with the same initial condition can evolve in different ways and converge to a different asymptotic behavior. For this reason, even the exact knowledge of the initial conditions does not necessarily lead to the predictability of the final state of the system. Hence, the noise can be considered as an important source of unpredictability that cannot be fully understood using the conventional methods of nonlinear dynamics, such as the exit basins and the uncertainty exponent. By adopting a probabilistic point of view, we develop the concepts of probability basin, uncertainty basin and noise-sensitivity exponent, that allow us to carry out both a quantitative and qualitative analysis of the unpredictability on noisy chaotic scattering problems.
Measuring the transition between nonhyperbolic and hyperbolic regimes in open Hamiltonian systems
(Springer, 2020) Nieto, Alexandre R.; Zotos, Euaggelos E.; Seoane, Jesús M.; Sanjuán, Miguel A.F.
We show that the presence of KAM islands in nonhyperbolic chaotic scattering has deep implications on the unpredictability of open Hamiltonian systems. When the energy of the system increases, the particles escape faster. For this reason, the boundary of the exit basins becomes thinner and less fractal. Hence, we could expect a monotonous decrease in the unpredictability as well as in the fractal dimension. However, within the nonhyperbolic regime, fluctuations in the basin entropy have been uncovered. The reason is that when increasing the energy, both the size and geometry of the KAM islands undergo abrupt changes. These fluctuations do not appear within the hyperbolic regime. Hence, the fluctuations in the basin entropy allow us to ascertain the hyperbolic or nonhyperbolic nature of a system. In this manuscript, we have used continuous and discrete open Hamiltonian systems in order to show the relevant role of the KAM islands on the unpredictability of the exit basins, and the utility of the basin entropy to analyze this kind of systems.
Noise activates escapes in closed Hamiltonian systems
(Elsevier, 2022) Nieto, Alexandre R.; Seoane, Jesús M.; Sanjuán, Miguel A.F.
In this manuscript we show that a noise-activated escape phenomenon occurs in closed Hamiltonian systems. Due to the energy fluctuations generated by the noise, the isopotential curves open up and the particles can eventually escape in finite times. This drastic change in the dynamical behavior turns the bounded motion into a chaotic scattering problem. We analyze the escape dynamics by means of the average escape time, the probability basins and the average escape time distribution. We obtain that the main characteristics of the scattering are different from the case of noisy open Hamiltonian systems. In particular, the noise-enhanced trapping, which is ubiquitous in Hamiltonian systems, does not play the main role in the escapes. On the other hand, one of our main findings reveals a transition in the evolution of the average escape time insofar the noise is increased. This transition separates two different regimes characterized by different algebraic scaling laws. We provide strong numerical evidence to show that the complete destruction of the stickiness of the KAM islands is the key reason under the change in the scaling law. This research unlocks the possibility of modeling chaotic scattering problems by means of noisy closed Hamiltonian systems. For this reason, we expect potential application to several fields of physics such us celestial mechanics and astrophysics, among others.
Period-doubling bifurcations and islets of stability in two-degree-of-freedom Hamiltonian systems
(American Physical Society (APS), 2023) Nieto, Alexandre R.; Seoane, Jesús M.; Sanjuán, Miguel A.F.
In this paper, we show that the destruction of the main Kolmogorov-Arnold-Moser (KAM) islands in two-degree-of-freedom Hamiltonian systems occurs through a cascade of period-doubling bifurcations. We calculate the corresponding Feigenbaum constant and the accumulation point of the period-doubling sequence. By means of a systematic grid search on exit basin diagrams, we find the existence of numerous very small KAM islands (“islets”) for values below and above the aforementioned accumulation point. We study the bifurcations involving the formation of islets and we classify them in three different types. Finally, we show that the same types of islets appear in generic two-degree-of-freedom Hamiltonian systems and in area-preserving maps.
Resonant behavior and unpredictability in forced chaotic scattering
(American Physical Society (APS), 2018) Nieto, Alexandre R.; Seoane, Jesús M.; Alvarellos, J. E.; Sanjuán, Miguel A.F.
Chaotic scattering in open Hamiltonian systems is a topic of fundamental interest in physics, which has been mainly studied in the purely conservative case. However, the effect of weak perturbations in this kind of system has been an important focus of interest in the past decade. In a previous work, the authors studied the effects of a periodic forcing in the decay law of the survival probability, and they characterized the global properties of escape dynamics. In the present paper, we add two important issues in the effects of periodic forcing: the fractal dimension of the set of singularities in the scattering function and the unpredictability of the exit basins, which is estimated by using the concept of basin entropy. Both the fractal dimension and the basin entropy exhibit a resonant-like decrease as the forcing frequency increases. We provide a theoretical reasoning which could justify this decreasing in the fractality near the main resonant frequency that appears for ω ≈ 1. We attribute the decrease in the basin entropy to the reduction of the area occupied by the Kolmogorov-Arnold-Moser (KAM) islands and the basin boundaries when the frequency is close to the resonance. On the other hand, the decay rate of the exponential decay law shows a minimum value of the amplitude, Ac, which reflects the complete destruction of the KAM islands in the resonance. Finally, we have found the existence of Wada basins for a wide range of values of the frequency and the forcing amplitude. We expect that this work could be potentially useful in research fields related to chaotic Hamiltonian pumps and oscillations in chemical reactions and companion galaxies, among others.
Systematic search for islets of stability in the standard map for large parameter values
(Springer, 2024-04-14) Nieto, Alexandre R.; Capeáns, Rubén; Sanjuan, Miguel A.F.
In the seminal paper, Chirikov (Phys Rep 52:263–379, 1979) showed that the standard map does not exhibit a boundary to chaos, but rather that there are small islands (“islets”) of stability for arbitrarily large values of the nonlinear perturbation. In this context, he established that the area of the islets in the phase space and the range of parameter values where they exist should decay following power laws with exponents and , respectively. In this paper, we carry out a systematic numerical search for islets of stability and we show that the power laws predicted by Chirikov hold. Furthermore, we use high-resolution 3D islets to reveal that the islets’ volume decays following a similar power law with exponent -3
Trapping enhanced by noise in nonhyperbolic and hyperbolic chaotic scattering
(Elsevier, 2021) Nieto, Alexandre R.; Seoane, Jesús M.; Sanjuán, Miguel A. F.
The noise-enhanced trapping is a surprising phenomenon that has already been studied in chaotic scattering problems where the noise affects the physical variables but not the parameters of the system. Following this research, in this work we provide strong numerical evidence to show that an additional mechanism that enhances the trapping arises when the noise influences the energy of the system. For this purpose, we have included a source of Gaussian white noise in the HȨnon-Heiles system, which is a paradigmatic example of open Hamiltonian system. For a particular value of the noise intensity, some trajectories decrease their energy due to the stochastic fluctuations. This drop in energy allows the particles to spend very long transients in the scattering region, increasing their average escape times. This result, together with the previously studied mechanisms, points out the generality of the noise-enhanced trapping in chaotic scattering problems.