# Stability, typicality and rigidity in smooth dynamics

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · University of Chicago (IL) · $300,000

## Abstract

This project explores why some systems behave predictably while others react chaotically to even the slightest nudge — a question with consequences for everything from weather forecasting to data security. By uncovering the mathematical rules that govern the coexistence of order and chaos, the work strengthens the nation’s scientific knowledge base and supports future technological innovation. Findings will be shared widely through public lectures, podcasts, and a forthcoming graduate-level book, “Dynamics, Rigidity, and Geometry,” making cutting-edge ideas accessible to students, educators, and lifelong learners.

The research tackles three intertwined themes in smooth dynamics:

1.	Stability. Identify mechanisms that keep chaotic or regular behavior intact under small perturbations. A major target is the symplectic C1 ergodic hypothesis, with new perturbation and blender techniques expected to yield density results for stably ergodic symplectomorphisms.

2.	Typicality. Determine which dynamical properties occur for “most’’ systems. Work on expanding and unstable foliations aims to prove openness and density of minimal strong foliations and to establish uniqueness of associated equilibrium (u-Gibbs) measures, with consequences for their higher statistical properties.

3.	Rigidity. Classify maps that possess large symmetry groups. The project’s “affine centralizer program” links the algebraic size of a diffeomorphism’s centralizer to its long-term dynamics, producing 

## Key facts

- **NSF award ID:** 2452616
- **Awardee organization:** University of Chicago (IL)
- **SAM.gov UEI:** ZUE9HKT2CLC9
- **PI:** Anne M Wilkinson
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** —
- **Estimated total:** $300,000
- **Funds obligated:** $300,000
- **Transaction type:** Standard Grant
- **Period:** 07/15/2025 → 06/30/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2452616

## Citation

> US National Science Foundation, Award 2452616, Stability, typicality and rigidity in smooth dynamics. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2452616. Licensed CC0.

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