A completeness result for time-dependent vector fields and applications

DOI10.1142/S0219199714500400zbMath1361.58003MaRDI QIDQ5264565

Andrea Bonfiglioli, Stefano Biagi

Publication date: 27 July 2015

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

Hörmander vector fieldsCarnot-Carathéodory metriccompleteness of vector fieldsCampbell-Baker-Hausdorff-Dynkin theoremthird theorem of Lie

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Control problems involving ordinary differential equations (34H05) Lie algebras of Lie groups (22E60) Vector distributions (subbundles of the tangent bundles) (58A30)

Related Items (6)

Global estimates for the fundamental solution of homogeneous Hörmander operators ⋮ Non-divergence operators structured on homogeneous Hörmander vector fields: heat kernels and global Gaussian bounds ⋮ Global Gaussian estimates for the heat kernel of homogeneous sums of squares ⋮ Large sets at infinity and maximum principle on unbounded domains for a class of sub-elliptic operators ⋮ Global estimates in Sobolev spaces for homogeneous Hörmander sums of squares ⋮ On the Baker-Campbell-Hausdorff Theorem: non-convergence and prolongation issues

Cites Work

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• Matrix-exponential groups and Kolmogorov-Fokker-Planck equations
• Global \(L^{p}\) estimates for degenerate Ornstein-Uhlenbeck operators
• Topics in noncommutative algebra. The theorem of Campbell, Baker, Hausdorff and Dynkin
• An ODE's version of the formula of Baker, Campbell, Dynkin and Hausdorff and the construction of Lie groups with prescribed Lie algebra
• Balls and metrics defined by vector fields. I: Basic properties
• Extending the Campbell-Hausdorff multiplication
• Lie groups related to Hörmander operators and Kolmogorov-Fokker-Planck equations
• Control systems on Lie groups
• Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung
• Introduction to Smooth Manifolds
• The “Bang-Bang” Problem for Certain Control Systems in $GL(n,R)$

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