The Binder-DeMarco-Dupont Inequality
In the setting of endomorphisms of $\mathbb{P}^k(\mathbb{C})$, a dimension formula for the measure of maximal entropy was conjectured by Binder and DeMarco in 2003, asserting that $$\mathrm{dim}_\mathrm{Hausdorff}(\mu)=\log d\sum_{i=1}^k \frac{1}{\chi_i},$$ where $d$ is the degree of the (non-invertible) endomorphism and $\chi_i$'s are the Lyapunov exponents with multiplicity. Indeed, this is well-defined as all Lyapunov exponents are known to be positive due to Briend and Duval. The most significant progress is due to Dupont, who in complex-dimension 2, proved the dimension lower-bound…
Comments and reviews
No comments yet.
API
curl /api/v1/records/hexagon/2610.00418
curl -X POST /api/v1/records/hexagon/2610.00418/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2610.00418/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'