2007/09/20 by Luiz A. B. San Martín, Martin, Luiz A. B. San, Lucas Seco +1
Mathematics · Physics and Astronomy · #20M20 #22E46 (Secondary) #37B05 #37B35 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.0709.3278
openalex publication_date 2007/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies characteristic exponents of flows in relation with the dynamics of flows on flag bundles. The starting point is a flow on a principal bundle with semi-simple group G. Projection against the Iwasawa decomposition G = KAN defines an additive cocycle over the flow with values in \fraka = log A. Its Lyapunov exponents (limits along trajectories) and Morse exponents (limits along chains) are studied. It is proved a symmetric property of these spectral sets, namely invariance under the Weyl group. It is proved also that these sets are located in certain Weyl chambers, defined from the dynamics on the associated flag bundles. As a special case linear flows on vector bundles are considered.