[Todos CMAT] Finite-time generalized high-order Lyapunov exponents for kicked double rotor _ charla prof. visitante Rodrigo Pereira

[Lydia Tappa]

*Miércoles 18 a las 15:00hs** en el salón de seminarios del Instituto de
Física de la Facultad de Ciencias* (IFFC)

Rodrigo F. Pereira

Federal University of Technology – Paraná

The ordinary Lyapunov exponents spectrum describes the average exponential
expansion/shrinkage rates of the axis of an infinitesimal ball around a
trajectory under the temporal evolution of a dynamical system. These
exponents are given by the linearization of the ruling equations. Due to
intrinsic nonlinearities present in models that present chaotic dynamics,
nonlinear effects, swept off by the linearization, can be crucial in
elucidating details of the temporal evolution of such systems. Moreover,
since Lyapunov exponents are dynamic invariants computed as an average over
an ergodic trajectory, they are ”blind” about local/finite-time
fluctuations present in typical chaotic dynamical systems. We present a
detailed analysis of the finite-time fluctuations of the generalized
high-order Lyapunov exponents for a physical system composed of a
periodically kicked double rotor. We focus in its chaotic regime and in the
transition from chaos to hyper-chaos as the intensity of the kicks is
increased. Generalized high-order Lyapunov exponents are given by the
analysis of high-order derivatives of the dynamical equations, which define
linear mappings and their effects over the Lyapunov vectors are studied in
a similar manner done for ordinary Lyapunov exponents. We study the
temporal fluctuations of these high-order Lyapunov exponents for
finite-time trajectories and relate their properties with those observed in
the chaos / hiper-chaos transition.



El Dr. Rodrigo F. Pereira pertenece al Departamento de Matemática de la
Universidad Tecnológica Federal de Paraná (UTFPR), Brasil, donde se
desempeña como Profesor Adjunto desde el 2013. Su trabajo se centra en el
estudio de sistemas dinámicos acoplados, con énfasis en la caracterización
y desarrollo del caos y la sincronización [e.g., Commun. Nonlinear Sci.
Numer. Simul. *18*, 1491-1498 (2013), Phys. Rev. E *86*, 016216(4) (2012),
Phys. Rev. E *83*, 037201(4) (2011)].

En particular, la charla que presentará el *Miércoles 18 a las 15:00hs** en
el salón de seminarios del Instituto de Física de la Facultad de Ciencias*
(IFFC), tratará sobre la generalización de ciertos indicadores (i.e., los
exponentes de Lyapunov) utilizados comunmente para caracterizar el
comportaminento de un sistema dinámico no-lineal. El Dr. Rodrigo F. Pereire
estará visitando el IFFC desde el 16 al 25 de Noviembre.
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