Mauro Patrão
Lyapunov, metric and flag spectra.
Wed, 12/09/2009 - 16:01 — SomNambulAuthors: Mauro Patrão
Subjects: Dynamical Systems
AbstractWe introduce the \emph{metric spectrum}, which measures the exponential rate
of approximation to an isolated invariant set of points starting in its stable
set, and relate it to the Lyapunov spectrum. We determine the metric spectrum
of each Morse component of the finest Morse decomposition of a linear induced
flow on a generalized flag manifold.An elementary proof of the uniqueness of the solutions of linear odes.
Fri, 10/09/2009 - 18:27 — SomNambulAuthors: Mauro Patrão
Subjects: General Mathematics
AbstractIn this note, we present an elementary proof of the uniqueness of the
solutions of the initial value problems of linear ordinary differential
equations (odes).An elementary proof of the robustness of the linear hyperbolic flows.
Tue, 09/22/2009 - 14:09 — SomNambulAuthors: Mauro Patrão
Subjects: General Mathematics
AbstractWe present an elementary proof that the qualitative picture of a linear
hyperbolic flow is insensitive to slight measurements errors in its associated
vector field.A note on periodic differential equations.
Fri, 08/21/2009 - 19:51 — SomNambulAuthors: Mauro Patrão
Subjects: Dynamical Systems
AbstractLet $F$ be a Banach space and $L(F)$ be the set of all its bounded linear
operators. In this note, we are interested in the asymptotic behavior
(recurrence and chain recurrence) of the solution of the following initial
value problem \label{eqlinear} x'(t) = X(t)x(t), \qquad x(0) = x, where $x \in
F$ and the map $t \mapsto X(t) \in L(F)$ is a $T$-periodic continuous curve.
This asymptotic behavior is related to the asymptotic behavior of the
discrete-time flow on $F$ generated by the invertible operator $g \in L(F)$
given by the associated fundamental solution at time $T$.
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