Seyed Ata Tahuri Turki

Dynamical Systems and Ergodic Theory

I am a Ph.D. candidate in Mathematics at The Pennsylvania State University.

My research lies in dynamical systems and ergodic theory, with a particular focus on partially hyperbolic systems, invariant measures, Lyapunov exponents, and the statistical behavior of nonlinear dynamical systems.

Broadly speaking, I study how deterministic systems that may exhibit chaotic behavior can nevertheless possess predictable long-term statistical patterns.

Research Interests

• Partially hyperbolic dynamical systems
• Ergodic theory
• Invariant and physical measures
• SRB and (u)-Gibbs measures
• Lyapunov exponents
• Smooth rigidity
• Mathematical models of complex systems

Current Research

My current research concerns structural relationships between (u)-Gibbs measures and SRB measures in partially hyperbolic systems.

A partially hyperbolic system admits an invariant splitting

\[ TM=E^s\oplus E^c\oplus E^u, \]

where different directions exhibit different rates of contraction or expansion.

I am especially interested in understanding when invariant measures describe observable long-term behavior and how geometric properties of invariant foliations influence statistical stability.— title: “atatahuri-website” —

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