IMJ-PRG |
Géométrie et Dynamique |
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Correction to Nakamoto's foundational Bitcoin paper (2008) and close-form formula for the probability of success of a double spend attack.
Explaining A. Selberg's analogy (1956) between Explicit Formulas in Number Theory and Trace Formulas.
Realizing geometrically real homology classes and giving a geometric form of De Rham Theorem (1931).
Extending the zeta product regularization in order to compute the product of primes that is found to be 4π2 answering a question of Ch. Soulé (1992).
Dichotomic answer on the question of H. Eliasson and J. Moser about the convergence of Birkhoff normal form.
Extending a result of Y. Ilyashenko from the cohomological equation to the non-linearized problem.
Discovery of hedgehogs associated to indifferent fixed points in holomorphic dynamics and its applications to the solution of several classical problems from H. Dulac (1904), C.-L. Siegel (1956), R. Moussu (1991), etc.
Construction of uncountable abelian groups of non-linearizable dynamics with applications to solution of question of H. Rosenberg and W. Thurston (1971), and J. Moser and M.R. Herman (1980).
Application of hedgehogs to the solution of a problem from P. Fatou (1918), H. Dulac (1904), and C. Briot and J.-C. Bouquet (1856).
Solution to the V. I. Arnold Conjecture of the accumulation by small cycles for non-linearizable circle diffeomorphisms (1958) and P. Sad conjecture (1980) for holomorphic germs.
