Lecture  4 (video-conf)

6 Maio 2020, 14:30 • Maria Teresa Faria da Paz Pereira

Equilibria; linearization about equilibria.
Linear autonomous DDEs x'(t)=L(x_t); characteristic equation; properties of the roots of the characteristic equation.
Location of the roots and result on stability for linear DDEs. Linearisation about equilibria and principle of linearised stability for hyperbolic equilibria.

Characteristic equations for linear autonomous DDEs and applications to some concrete examples.

Theory of Hille-Phillips for C_0 semigroups of linear operators in Banach spaces applied to linear DDEs: the solution operator for x'(t)=L(x_t) is a C_0 semigroup; infinitesimal generator. Exponential behaviour and connection with the sprectrum of the infinitesimal generator via the Hille-Phillip theory (basic ideas for proof).

This lecture took place on May 12, from 17h to 18h45.

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