# Applications

## Problem 132

$\dot X = Q(X)$ on $\mathbb{R}^3$, where $Q$ is quadratic. Is there a condition on the coefficients which guarantees a homoclinic point (a complicated attractor)? E.g. like for Reynolds numbers?

## Problem 92

Among degree $n$ polynomial maps of $[0,1]$ to itself, are Axiom A open and dense. Do bad ones form a stratified set? ...

## Problem 85

codon frequencies via equilibrium states for some potential''?

## Problem 84

Invariant or approximatively invariant finite dimensional subspaces for Navier-Stokes equation

## Problem 78

Calculate $h$ for O.D.E. systems on $\mathbb{R}^n$, e.g. linear equations first

## Problem 68

Electric circuits

• Analogue computer for finding Axiom A examples
• Is noise sometimes due to hyperbolicity in the dynamics?

## Problem 67

Correspondence principle of quantum mechanics. Investigate for some simple mechanical systems. Is h-expansiveness related to quantum ....?

## Problem 59

Computer programs for Axiom A attractor.

## Problem 58

Is Gutzwiller's example an Anosov flow?

## Problem 46

Equilibrium states for 1-dimensional quantum lattice systems without finite range

## Problem 42

Is $h(\varphi_t | E)$ differentiable in $E$ for Hamiltonian flows? Any relation to classical or quantum statistical mechanics?

## Problem 29

Find Axiom A infinite attractor in some O.D.E. on $\mathbb{R}^3$ (quadratic).

## Problem 26

Entropy in Hamiltonian case; for P.D.E.'s? Relation to O.D.E.'s?