We prove that the Birkhoff normal form of hamiltorlian flows at a nonresonant singular point with given quadratic part is always convergent or generically divergent. The same result is proved for the… Expand

We correct the double spend race analysis given in Nakamoto's foundational Bitcoin article and give a closed-form formula for the probability of success of a double spend attack using the Regularized Incomplete Beta Function.Expand

We review the so called selfish mining strategy in the Bitcoin network and compare its profitability to honest mining even after a difficulty adjustment.Expand

We study selfish mining in Ethereum. The problem is combinato-rially more complex than in Bitcoin because of major differences in the reward system and a different difficulty adjustment formula.… Expand

Abstract: We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. The characteristic features are delicate problems of convergence of… Expand

Bitcoin is the first decentralized peer-to-peer (P2P) electronic currency. It was created in November 2008 by Satoshi Nakamoto. Nakamoto released the first implementation of the protocol in an open… Expand

Nakamoto double spend strategy, described in Bitcoin foundational article, leads to total ruin with positive probability and does not make sense from the profitability point of view.Expand