The Romanian side of the project is financed by The Executive Unit for Financing Higher Education, Research, Development and Innovation (UEFISCDI), Romania. The project has a duration of three years, 2025-2028. The host institution is the "Simion Stoilow" Institute of Mathematics of the Romanian Academy (IMAR). The American side of the project is financed by the NSF.
The field of dynamics studies how processes evolve over time, such as the motion of planets,
population growth, or the behavior of digital networks. The mathematical theory of dynamical
systems offers a powerful language to describe these changes, uncover patterns, predict future
behavior, and identify when systems may become chaotic. One-dimensional holomorphic dynamics is a
mature field of mathematics, rooted in the famous work of Fatou and Julia on fractal sets. In contrast,
higher-dimensional holomorphic dynamics is a newer but rapidly developing area, marked by fundamentally
different behavior and rich phenomena absent in the one-dimensional setting. The PIs will advance understanding
of dynamical systems in several complex variables by bridging this gap between dimension one and higher dimensions.
The project will also provide training opportunities for graduate students and postdoctoral researchers. This is a
project funded jointly by the National Science Foundation's Division of Mathematical Sciences, in the Directorate
for Mathematical and Physical Sciences, and the Romanian Executive Agency for Higher Education, Research, Development
and Innovation Funding (UEFISCDI), in accordance with the Memorandum of Understanding between the NSF and UEFISCDI.
The PIs will investigate the dynamics of higher-dimensional germs of holomorphic diffeomorphisms,
particularly those with neutral fixed points, which pose unique challenges. A key goal is to characterize
the structure of the dynamical system near the fixed points and to extend concepts like hedgehogs - intricate
invariant sets from one-dimensional dynamics - to higher dimensions, especially in the setting of conservative
holomorphic germs. The PIs will also analyze the dynamics and bifurcations of polynomial automorphisms of two-dimensional
complex space, with particular attention to the relationship between Julia sets and critical loci-sets of tangencies
between dynamically defined foliations. The research activity conducted under this award will generate pioneering techniques
in higher-dimensional dynamics, with impact in other areas of mathematics such as topology and geometry.