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E. B. Vul is a coauthor, with Yakov Sinai and Konstantin Khanin, of a 1984 study of Feigenbaum constants using thermodynamic formalism. The work connects the scaling behavior of period doubling with methods developed for statistical mechanics. The initials identify the cited byline; they are retained here without assuming an unverified expansion of the name.^[ref]

By E. B. Vul, Yakov Sinai, Konstantin Khanin.

Russian Mathematical Surveys 39(3), pages 1–40.

By Uriel Frisch, Konstantin Khanin, Takeshi Matsumoto.

Journal of Statistical Physics 121, pages 671–695.

Preprint: arxiv.org/abs/nlin/0309068

Takeshi Matsumoto studied the multifractal measure of the Feigenbaum attractor with Uriel Frisch and Konstantin Khanin. Their analysis related power-law tails of fractional derivatives of an integrated invariant measure to its spectrum of local singularities.^[ref]

This supplies a way to detect nonuniform scaling from a transformed observable, rather than assigning the entire attractor one local exponent. The paper distinguishes its heuristic theoretical steps from high-accuracy numerical checks.

Uriel Frisch studied nonuniform scaling of invariant measures with Konstantin Khanin and Takeshi Matsumoto. Their work on the Feigenbaum attractor related the statistics of fractional derivatives to the local singularity structure of a multifractal measure.^[ref]

A single fractal dimension need not describe how probability concentrates differently from point to point. The derivative-based test offers another way to probe that spatially varying scaling, with the paper explicitly comparing heuristic arguments and precise numerical calculations.

Yakov Sinai contributed to the study of Feigenbaum constants through thermodynamic formalism, in joint work with E. B. Vul and Konstantin Khanin. Their 1984 paper connects universal period-doubling scaling with methods of statistical mechanics, illustrating how probabilistic and geometric descriptions of a dynamical system can reinforce each other.^[ref]