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Explore the intersection of computation and dynamical systems in this 47-minute conference talk that examines how mathematical dynamical systems can be utilized as computational frameworks. Delve into the theoretical foundations and practical applications of using continuous dynamical processes to perform calculations and solve computational problems. Learn about the mathematical principles underlying dynamical computation, including how differential equations and iterative systems can represent and execute algorithms. Discover the connections between traditional discrete computation and continuous dynamical approaches, examining both the advantages and limitations of each paradigm. Investigate specific examples of dynamical systems that can perform computational tasks, from simple arithmetic operations to more complex algorithmic processes. Understand the theoretical implications for computational complexity theory and how dynamical systems might offer alternative approaches to classical computational models. Gain insights into current research directions in this emerging field that bridges mathematics, computer science, and physics, and consider the potential future applications of dynamical computation in solving real-world problems.
