The fundamental theorem of tropical differential algebra for formal Puiseux series

The fundamental theorem of tropical differential algebra has been established for formal power series solutions of systems of algebraic differential equations. It has been shown that the direct extension to formal Puiseux series solutions fails. In this paper, we overcome this issue by transforming the given differential system and such a generalization is presented. Moreover, we explain why such transformations do not work for generalizing the fundamental theorem to transseries solutions, but show that one inclusion still holds for this case even without using any transformation. 2010 Mathematics Subject Classification. Primary 14A20; Secondary 12H99, 13N99, 14T05, 14T99.