Stickiness effects in chaos

Contopoulos, G.; Harsoula, M.

doi:10.1007/s10569-010-9282-6

Cited by 57 publications

(44 citation statements)

References 21 publications

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“…Kovács and Érdi 2009;Contopoulos and Harsoula 2010) around the main stability island. In the case of the regular component, we have invariant curves.…”

Section: Study Of Some Representative Orbits Through the Cis' Time Evmentioning

confidence: 99%

A comparison of different indicators of chaos based on the deviation vectors: application to symplectic mappings

Maffione

Darriba

Cincotta

et al. 2011

Celest Mech Dyn Astr

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The aim of this research work is to compare the reliability of several variational indicators of chaos in mappings. The Lyapunov Indicator; the Mean Exponential Growth factor of Nearby Orbits (MEGNO); the Smaller Alignment Index (SALI); the Fast Lyapunov Indicator (FLI); the Dynamical Spectra of stretching numbers and the corresponding Spectral Distance and the Relative Lyapunov Indicator (RLI), which is based on the evolution of the difference between two close orbits, have been included. The experiments presented herein allow us to reliably suggest a group of chaos indicators to analyze a general mapping. We show that a package composed of the FLI and the RLI (to analyze the phase portrait globally) and the MEGNO and the SALI (to analyze orbits individually) is good enough to make a description of the systems' dynamics.

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“…Kovács and Érdi 2009;Contopoulos and Harsoula 2010) around the main stability island. In the case of the regular component, we have invariant curves.…”

Section: Study Of Some Representative Orbits Through the Cis' Time Evmentioning

confidence: 99%

A comparison of different indicators of chaos based on the deviation vectors: application to symplectic mappings

Maffione

Darriba

Cincotta

et al. 2011

Celest Mech Dyn Astr

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“…Therefore the stickiness of phase trajectories has a crucial influence on the transport properties of Hamiltonian systems, and its relation to physical systems is one of the most important open problems of nonlinear dynamics [4,5]. Applications of stickiness can be found in astronomy [6], fluid mechanics [7], Levy flights [8], also in biology [9], in plasma physics [10,11], and many others.…”

Section: Introductionmentioning

confidence: 99%

Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

et al. 2012

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Some phase space transport properties for a conservative bouncer model are studied. The dynamics of the model is described by using a two-dimensional measure preserving mapping for the variables' velocity and time. The system is characterized by a control parameter and experiences a transition from integrable ( = 0) to nonintegrable ( = 0). For small values of , the phase space shows a mixed structure where periodic islands, chaotic seas, and invariant tori coexist. As the parameter increases and reaches a critical value c , all invariant tori are destroyed and the chaotic sea spreads over the phase space, leading the particle to diffuse in velocity and experience Fermi acceleration (unlimited energy growth). During the dynamics the particle can be temporarily trapped near periodic and stable regions. We use the finite time Lyapunov exponent to visualize this effect. The survival probability was used to obtain some of the transport properties in the phase space. For large , the survival probability decays exponentially when it turns into a slower decay as the control parameter is reduced. The slower decay is related to trapping dynamics, slowing the Fermi Acceleration, i.e., unbounded growth of the velocity.

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“…they remain close to their average initial distances for quite long times. The phenomenon of stickiness of chaotic orbits has been discussed by Contopoulos and Harsoula (2010) with particular emphasis on sticky chaotic orbits in barred galaxies.…”

Section: Resonant Orbits and Diffusion Timesmentioning

confidence: 99%

Chaotic spiral galaxies

Contopoulos

Harsoula

2011

Celest Mech Dyn Astr

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We study the role of asymptotic curves in supporting the spiral structure of a N-body model simulating a barred spiral galaxy. Chaotic orbits with initial conditions on the unstable asymptotic manifolds of the main unstable periodic orbits follow the shape of the periodic orbits for an initial interval of time and then they are diffused outwards along the spiral structure of the galaxy. Chaotic orbits having small deviations from the unstable periodic orbits, stay close and along the corresponding unstable asymptotic manifolds, supporting the spiral structure for more than 10 rotations of the bar. Chaotic orbits of different Jacobi constants support different parts of the spiral structure. We also study the diffusion rate of chaotic orbits outwards and find that the orbits that support the outer parts of the galaxy are diffused outwards more slowly than the orbits supporting the inner parts of the spiral structure.

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Stickiness effects in chaos

Cited by 57 publications

References 21 publications

A comparison of different indicators of chaos based on the deviation vectors: application to symplectic mappings

A comparison of different indicators of chaos based on the deviation vectors: application to symplectic mappings

Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

Chaotic spiral galaxies

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