Henri Poincare’s legacy for tipping points

The science of Earth system and climate tipping points has evolved and matured as a disciplined approach to understanding anthropogenic and non-anthropogenic stresses on the Earth’s subsystems in the 21^st century. However, tipping points is strongly interlinked with the science of bifurcations and dynamical systems, which received a seminal and resonant illumination by the great French mathematician Henri Poincare (1854-1912). Thus, quite a few historically minded tipping point scientists mention Poincare as the seminal, path-setting thinker for tipping point understandings.

Moreover, Poincare’s bifurcation and dynamical systems-pertinent science is also linked to his seminal role in chaos theory, which illuminates today’s understanding of climate stochasticity. Poincare famously said, "A very small cause which escapes us determines a considerable effect that we cannot see; so, we say this effect is random," which provided grounding for the chaos notion of critical sensitivity to initial conditions. Since Poincare, great strides in abrupt change understanding as linked to chaos (and within an examination of turbulence) have taken place in the science that informs tipping points, such as with the work of Ed Lorenz and David Ruelle. Additionally, the Russian mathematicians (e.g., Andronov and Arnold) have contributed greatly with the refining of differential equations for bifurcation understandings that Poincare began.  

This EGU presentation is a history of science presentation on Henri Poincare's commencement of bifurcation, dynamical system and chaos understandings as presented by a journalist who has done both interviews and general historical research. The presentation sets key points in Poincare’s biography and pertinent career and sketches the legacy of this Poincare focus up from Henri Poincare through Russian bifurcation scientists, catastrophe theorist Rene Thom, and ultimately Lorenz and current bifurcation theorists, such as Michael Ghil and Valerio Lucarini. It offers light on the ancestry of one of the most important examinations of the Anthropocene, climate change tipping points.