A (short) survey on Dominated Splitting

Abstract

We present here the concept of Dominated Splitting and give an account of some important results on its dynamics.

19 pages

References in corpus (4)

• Dominated Splitting and Pesin's Entropy Formula
• Stably ergodic diffeomorphisms which are not partially hyperbolic
• Tangent bundles dynamics and its consequences
• Internal perturbations of homoclinic classes:non-domination, cycles, and self-replication

Cited by in corpus (8)

• Differences and similarities in the analysis of Lorenz, Chen, and Lu systems
• Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations
• Symplectic Geometry of Anosov Flows in Dimension 3 and Bi-Contact Topology
• Vortices over Riemann surfaces and dominated splittings
• Topological and geometric hyperbolicity criteria for polynomial automorphisms of C^2
• Conformality for a robust class of non-conformal attractors
• Characterization of uniform hyperbolicity for fiber-bunched cocycles
• Formula of Entropy along Unstable Foliations for $C^1$ Diffeomorphisms with Dominated Splitting