The theory of tropical series, that we develop here, firstly appeared in the study of the growth of pluriharmonic functions. Motivated by waves in sandpile models we introduce a dynamic on the set of tropical series, and it is experimentally observed that this dynamic obeys a power law. So, this paper serves as a compilation of results we need for other articles and also introduces several objects interesting by themselves.
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Figure 2.
First row shows how curves given by
Figure 3.
On the left:
Figure 5.
Examples of balancing condition in local pictures of tropical curves near vertices. The notation
Figure 6.
Left: the curve corresponding to the function
Figure 7.
Above pictures show non-unimodular corners
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