N.-Y.: Springer, 1997. - 673p.
Монография посвящена вопросам нелинейной динамики, как
теоретико-функциональным свойствам, так и приложениям в области
гидродинамики, химии, биологии и др. Рассматриваются плохо
определённые проблемы, неустойчивые многообразия, функции Ляпунова,
оценивание размерности. Основной интерес уделяется системам
бесконечной размерности.
Для изучающих хаотическую динамику и её приложения. Contents:
General results and concepts on invariant sets and attractors.
Elements of functional analysis.
Attractors of the dissipative evolution equation of the first order in time: reaction-diffusion equations.
Fluid mechanics and patte formation equations.
Attractors of dissipative wave equations.
Lyapunov exponents and dimensions of attractors.
Explicit bounds on the number of degrees of freedom and the dimension of attractors of some physical systems.
Non-well-posed problems, unstable manifolds. lyapunov functions, and lower bounds on dimensions.
The cone and squeezing properties.
Inertial manifolds.
Inertial manifolds and slow manifolds the nonselfadjoint case
Для изучающих хаотическую динамику и её приложения. Contents:
General results and concepts on invariant sets and attractors.
Elements of functional analysis.
Attractors of the dissipative evolution equation of the first order in time: reaction-diffusion equations.
Fluid mechanics and patte formation equations.
Attractors of dissipative wave equations.
Lyapunov exponents and dimensions of attractors.
Explicit bounds on the number of degrees of freedom and the dimension of attractors of some physical systems.
Non-well-posed problems, unstable manifolds. lyapunov functions, and lower bounds on dimensions.
The cone and squeezing properties.
Inertial manifolds.
Inertial manifolds and slow manifolds the nonselfadjoint case