A-flows with codimension-one basic sets

Key Points

• The aim is to describe the structure of codimension-one basic sets for flows satisfying Smale's Axiom A.
• Investigation of the structure of basic sets on closed manifolds of dimension n≥3.
• Construction of special trapping neighborhoods with specific topological features.
• Development of a compactification of the basin of a basic set.
• Extension of the original flow to the casing as a dynamical suspension.
• Codimension-one basic sets are classified as expanding attractors or contracting repellers.
• Trapping neighborhoods are identified as homeomorphic to ${\mathbb S}^{n-2} \times {\mathbb S}^1$.
• Compactification leads to a locally trivial fiber bundle structure over a circle.
• The extended flow maintains dynamical properties of structural stability.