Conference: Flexibility and Rigidity in Dynamical Systems

“动力系统中的灵活性和刚性”研讨会将于2022年3月7日至3月11日在石溪大学的西蒙斯几何与物理中心举行。动力系统模拟物理、生物或数学系统的时间演化，如行星运动、流体流动或疾病的进展。一些基本的概念和思想，如熵，混沌和吸引子，已经发展到描述这样的系统。符号动力学的工具在计算机科学中开发快速和安全的代码已被证明是重要的。双曲动力系统在电力系统及其网络问题中自然出现。它们在数学中也有应用，特别是在数论、数学物理和几何中。本次研讨会将汇集刚性和柔性动力系统领域的专家，以及大批研究生和年轻研究人员，开辟新的研究途径。主要目标是促进合作，建立一个研究动态中灵活性和刚性之间相互作用的研究人员社区。除了研究讲座和问题讨论外，研讨会还包括三门迷你课程。石溪靠近许多教育和研究机构，特别适合传播新的研究方向。研讨会将集中讨论双曲动力系统的精细性质，即轨道以指数速度发散的系统，因为它在许多情况下是典型的。数学家引入了不变量，特别是熵和李亚普诺夫指数，来描述它们的行为。人们可以很自然地要求这些不变量在给定一类动力系统中的取值范围（“灵活性”）。例如，当系统表现出额外的对称性时，这种范围可能是非常有限的。有时这会导致对系统的完整描述（“刚性”）。虽然对刚性的研究始于半个世纪前，但对灵活性的研究直到最近才开始。最近的研究亮点将成为研讨会迷你课程的核心，特别是在双曲动力系统的刚性，负弯曲流形的熵性质和群作用在圆上的灵活性方面的新进展。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The workshop "Flexibility and Rigidity in Dynamical Systems” will be held from March 7 to March 11, 2022 at the Simons Center for Geometry and Physics at Stony Brook University. Dynamical systems model the time evolution of physical, biological or mathematical systems, such as planetary motion, fluid flows, or the progression of diseases. Several fundamental concepts and ideas, such as entropy, chaos and attractors, have been developed to describe such systems. Tools from symbolic dynamics have proved important in developing fast and safe codes in computer science. Hyperbolic dynamical systems naturally arise in electrical systems and their network problems. They also have applications within mathematics, especially to number theory, mathematical physics and geometry. This workshop will bring together experts in the dynamical systems areas of rigidity and flexibility, as well as a large group of graduate students and young researchers, to open new research avenues. The primary goal is to foster collaboration and build a community of researchers engaged in studying the interplay between flexibility and rigidity in dynamics. The workshop includes three mini-courses in addition to research talks and a problem session. The proximity of Stony Brook to many education and research institutions lends itself particularly well to dissemination of new research directions. The workshop will focus on fine properties of hyperbolic dynamical systems, i.e., systems whose orbits diverge exponentially fast - as it is typical in many situations. Mathematicians introduced invariants, in particular entropy and Lyapunov exponents, to describe their behavior. One can naturally ask for the range these invariants can take in a given class of dynamical systems (“flexibility”). Such ranges can be very restrictive, for example, when the systems exhibit extra symmetries. Sometimes this leads to a complete description of the systems (“rigidity”). While investigations on rigidity started half a century ago, work on flexibility started only recently. Highlights of recent research will form the core of the mini-courses of the workshop, especially new advances on rigidity of hyperbolic dynamical systems, entropy properties of negatively curved manifolds, and flexibility of group actions on the circle. The conference website is at: http://scgp.stonybrook.edu/archives/33724This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.