A comparison of different indicators of chaos based on the deviation vectors. Application to symplectic mappings

The aim of this research work is to compare the reliability of several variational indicators of chaos on mappings. The Lyapunov Indicator (LI); 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 (SSN) and the corresponding Spectral Distance (D); 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.Comment: 25 pages, 40 figures. Celestial Mechanics and Dynamical Astronomy, in pres

On the relevance of chaos for halo stars in the Solar Neighbourhood

We show that diffusion due to chaotic mixing in the Neighbourhood of the Sun may not be as relevant as previously suggested in erasing phase space signatures of past Galactic accretion events. For this purpose, we analyse Solar Neighbourhood-like volumes extracted from cosmological simulations that naturally account for chaotic orbital behaviour induced by the strongly triaxial and cuspy shape of the resulting dark matter haloes, among other factors. In the approximation of an analytical static triaxial model, our results show that a large fraction of stellar halo particles in such local volumes have chaos onset times (i.e., the timescale at which stars commonly associated with chaotic orbits will exhibit their chaotic behaviour) significantly larger than a Hubble time. Furthermore, particles that do present a chaotic behaviour within a Hubble time do not exhibit significant diffusion in phase space.Comment: 20 pages, 16 figures. Accepted for publication in MNRA

Magnetic fabric of Pleistocene continental clays from the hanging-wall of an active low-angle normal fault (Altotiberina Fault, Italy)

Anisotropy of magnetic susceptibility (AMS) represents a valuable proxy able to detect subtle strain effects in very weakly deformed sediments. During the last decades a large number of AMS studies have documented that in compressive tectonic settings the maximum susceptibility axes (i.e. the magnetic lineations) are parallel to fold axes (and thrust faults) and local bedding strikes, while in extensional regimes they are perpendicular to the normal faults and, thus, parallel to the strata dip directions. One of the most striking active tectonic structures of the northern Apennines is represented by the Altotiberina Fault (ATF), a NE-dipping low-angle normal fault bounding the High Tiber Valley. The ATF represents a primary detachment of the Plio-Quaternary extensional tectonics affecting the Apennine belt. The long-lasting activity of the ATF produced 5 km of total displacement and up to 1200-m-thick basin infill of syn-tectonic, sandy-clayey continental succession. Thus, the AMS analysis of the sediments lying above the ATF represents a unique opportunity to document the strain field affecting the hanging-wall of low-angle normal faults. We collected 129 oriented cores at 12 different localities within the High Tiber Valley, and measured the AMS with a spinner Multi-Function Kappabridge. Most of the sites show a magnetic fabric typical of sediments at the earliest stages of deformation, characterized by oblate AMS ellipsoids and a well defined magnetic lineation, while prolate AMS ellipsoids at two sites are suggestive of pervasive tectonic effects. The magnetic lineation is well-developed at all sites and 20 has a prevailing N-S direction. At five sites the bedding is tilted and the magnetic lineation is subparallel to local bed-strikes, implying that these sites underwent a maximum horizontal shortening along an E-W direction. At two sites the magnetic lineation is sub-perpendicular to the trend of the ATF, and may be related to extensional strain. Our results reveal the existence of both compressional and extensional structures at the hangingwall of the ATF, and suggest that the early Pleistocene sequence of the High Tiber Valley is arranged in gently, local folds (hardly visible in the field) ~N-S trending. We interpret these compressivestructures as the result of local superficial stress induced by irregularities of the fault plane at depth. Accordingly, the strain field we documented from the High Tiber Valley can not be used to infer the regional tectonic regime acting during the ATF activity. We conclude that the long-lasting debate on the extensional vs. compressional Plio-Quaternary tectonics of the Apennines orogenic belt should be revised evaluating the importance of compressional structures resulting by local effects

Magnetic fabric of Pleistocene continental clays from the hanging-wall of an active low-angle normal fault (Altotiberina Fault, Italy)

Anisotropy of magnetic susceptibility (AMS) represents a valuable proxy able to detect subtle strain effects in very weakly deformed sediments. In compressive tectonic settings, the magnetic lineation is commonly parallel to fold axes, thrust faults, and local bedding strike, while in extensional regimes, it is perpendicular to normal faults and parallel to bedding dip directions. The Altotiberina Fault (ATF) in the northern Apennines (Italy) is a Plio-Quaternary NNW–SSE low-angle normal fault; the sedimentary basin (Tiber basin) at its hanging-wall is infilled with a syn-tectonic, sandy-clayey continental succession. We measured the AMS of apparently undeformed sandy clays sampled at 12 sites within the Tiber basin. The anisotropy parameters suggest that a primary sedimentary fabric has been overprinted by an incipient tectonic fabric. The magnetic lineation is well developed at all sites, and at the sites from the western sector of the basin it is oriented sub-perpendicular to the trend of the ATF, suggesting that it may be related to extensional strain. Conversely, the magnetic lineation of the sites from the eastern sector has a prevailing N–S direction. The occurrence of triaxial to prolate AMS ellipsoids and sub-horizontal magnetic lineations suggests that a maximum horizontal shortening along an E–W direction occurred at these sites. The presence of compressive AMS features at the hanging-wall of the ATF can be explained by the presence of gently N–Strending local folds (hardly visible in the field) formed by either passive accommodation above an undulated fault plane, or rollover mechanism along antithetic faults. The long-lasting debate on the extensional versus compressive Plio-Quaternary tectonics of the Apennines orogenic belt should now be revised taking into account the importance of compressive structures related to local effects

Timing of Tectonic and Magmatic Events in the Philippine Sea Plate Since 50 Ma From High-Resolution Magnetostratigraphy of IODP Site U1438

Abstract The Philippine Sea Plate in the West Pacific is a unique natural laboratory to study subduction dynamics and the evolution of upper plate magmatism following subduction initiation. To investigate these processes, International Ocean Discovery Program Expedition 351 recovered at Site U1438, located in a rear‐arc position, a complete sedimentary sequence from recent age to the early Eocene and the top of the underlying volcanic basement. The recovered cores offered the opportunity to study for the first time and in unprecedented detail the styles, products, and timing of the volcanic events that marked the emplacement, growth, and demise of the Kyushu‐Palau volcanic arc following the inception of the Izu‐Bonin‐Mariana subduction. Here, we report a magnetostratigraphy for Site U1438 based on ∼60,000 remanence directions isolated from 1,063 archive half core sections and 429 discrete specimens. We identified 142 magnetic reversals and correlated 115 of them with the geomagnetic polarity timescale. When combined with additional biostratigraphic and geochronological constraints, our magnetostratigraphy allowed construction of a high‐resolution age model for Site U1438 and the determination of changes in sedimentation rates. We show that following subduction initiation at 52–50 Ma and the emplacement of basalts in the rear‐arc at 48.7 Ma, a diffuse volcanism in the rear‐arc (48.4–45.6 Ma) preceded the true emplacement of the Kyushu‐Palau arc at 40.2 Ma, which then grew through four compositionally distinct eruptive phases until 28.8 Ma. Subsequent rollback of the Pacific slab triggered rifting of the arc (28.8–24.3 Ma) and ultimately back‐arc spreading in the Shikoku and Parece Vela basins

On the comparison of two different techniques for the study of chaos in galactic dynamics

Fil: Maffione, Nicolás P. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica de La Plata. CONICET; Argentina.Fil: Giordano, Claudia M. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica de La Plata. CONICET; Argentina.Fil: Cincotta, Pablo M. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaRealistic models in Galactic Dynamics seem to present a divided phase space (Giordano & Cincotta, 2004). Therefore, it is necessary to rely on efficient techniques to study the global dynamical behaviour in order to split as well as to identify the complex nature of the orbital structure. Herein we present some results of an exhaustive comparison between two of such techniques: the well–known Lyapunov characteristic exponents, and a rather new one, introduced by Cincotta & Simó (2000), the Mean Exponential Growth factor of Nearby Orbits (MEGNO).Los modelos realistas en Dinámica Galáctica parecen contar con un espacio de fases dividido (Giordano & Cincotta, 2004). Por lo tanto, es necesario disponer de técnicas eficientes para el estudio de la dinámica global, que separen e identifiquen la compleja naturaleza del movimiento orbital. En este trabajo se realizó una comparación exhaustiva entre dos de tales herramientas numéricas: una ya clásica, los exponentes característicos de Lyapunov, y otra más reciente, presentada por Cincotta & Simó (2000), el Mean Exponential Growth factor of Nearby Orbits (MEGNO)

Testeo del "MEGNO": indicador rápido de la dinámica

Fil: Maffione, Nicolás P. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. IALP-UNLP-CONICET; Argentina.Fil: Giordano, Claudia.Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. IALP-UNLP-CONICET; Argentina.Fil: Cincotta, Pablo.Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. IALP-UNLP-CONICET; Argentina.We extend a previous work (Maffione, Giordano & Cincotta, 2007) where the Lyapunov characteristic exponents and the Mean Exponential Growth factor of Nearby Orbits (MEGNO), introduced by Cincotta & Simó (2000), are compared. Some differences in their classifications appeared and one of the main possible causes of the discrepancy was discussed. Now, with the implementation of another technique closely related with the fast Lyapunov indicator (Froeschlé et al., 1997) and an analysis of the involved orbits’ neighborhoods, we understood the reasons for the discrepancy, reaching a detailed evaluation of the MEGNO efficiency.Extendemos un trabajo previo (Maffione, Giordano & Cincotta, 2007) donde se comparan los exponentes característicos de Lyapunov y el Mean Exponential Growth factor of Nearby Orbits (MEGNO), introducido por Cincotta & Simó (2000). Se observaron algunas diferencias en sus respectivas clasificaciones y se discutió una de las posibles causas de la discrepancia. Ahora, con la implementación de otra técnica estrechamente relacionada con el indicador rápido de Lyapunov (Froeschlé et al., 1997) y el análisis de los entornos de las órbitas involucradas, logramos entender el por qué de la discrepancia, obteniendo así una evaluación detallada del rendimiento del MEGNO