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## Ricardo Luiz Viana (Brazil)

# Chaotic bursting and the onset of unstable dimension variability

Dynamical systems possessing symmetries have invariant manifolds.
According to the transversal stability properties of this invariant manifold, nearby
trajectories may spend long stretches of time in its vicinity before being repelled
from it as a chaotic burst, after which the trajectories return to their
original laminar behavior. The onset of chaotic bursting is determined by the loss of
transversal stability of low-period periodic orbits embedded in the invariant
manifold, in such a way that the shadowability of chaotic orbits is broken due to
unstable dimension variability, characterized by finite-time Lyapunov exponents
fluctuating about zero. We use a two-dimensional map with an invariant subspace
to estimate shadowing distances and times from the statistical properties of the
bursts in the transversal direction. A stochastic model (biased random walk
with reflecting barrier) is used to relate the shadowability properties to the
distribution of the finite-time Lyapunov exponents.

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