We present a geometric, model-independent, argument that aims to explain why the Tsallis entropy describes systems exhibiting "weak chaos", namely systems whose underlying dynamics has vanishing largest Lyapunov exponent. Our argument relies on properties of a deformation map of the reals induced by the Tsallis entropy, and its conclusion agrees with all currently known results.Comment: 19 pages, Standard LaTeX2e, v2: addition of the last paragraph in Section 4. Three additional refs. To be published in QScience Connec
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