Lie and morse theory for periodic orbits of vector fields and matrix riccati equations, I: General lie-theoretic methods

DOI10.1007/BF01786984zbMath0508.58034MaRDI QIDQ4746552

Robert Hermann, Clyde F. Martin

Publication date: 1982

Published in: Mathematical Systems Theory (Search for Journal in Brave)

zbMATH Keywords

Morse theoryKilling vector fieldPoincare polynomialGrassmann pair

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items

The geometry of matrix eigenvalue methods ⋮ Partial differential systems with non-local nonlinearities: generation and solutions ⋮ The minimal Morse components of translations on flag manifolds are normally hyperbolic ⋮ Global observability of flows on the torus: An application of number theory ⋮ Grassmannian spectral shooting ⋮ Lie and Morse theory for periodic orbits of vector fields and matrix Riccati equations, II ⋮ On the Phase Portrait of the Fast Filtering Algorithms ⋮ Time-asymptotic dynamics of Hermitian Riccati differential equations

Cites Work

• Geometric aspects of potential theory in the bounded symmetric domains
• Differential geometry and the calculus of variations
• Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
• Fixed Points of Isometries
• Morse inequalities for a dynamical system
• Morse Theory. (AM-51)
• COMPACTIFICATIONS OF HOMOGENEOUS SPACES AND CONTRACTIONS OF LIE GROUPS
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