Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Arnold diffusion is a significant problem in dynamical systems and mathematical physics, discovered by Vladimir Arnold in 1963. Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom) result in topological instability. This proof is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.

\n Format: Paperback / softback
\n Length: 224 pages
\n Publication date: 03 November 2020
\n Publisher: Princeton University Press
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Arnold diffusion, a fundamental issue in dynamical systems and mathematical physics, has garnered significant attention since its discovery by Vladimir Arnold in 1963. This problem revolves around the emergence of chaos in classical mechanics. Since its inception, Arnold diffusion has attracted the dedication of renowned mathematicians, making it one of the most significant challenges in these fields. The central question revolves around whether a typical perturbation of a particular system leads to chaotic or unstable dynamical phenomena. In this groundbreaking work, Vadim Kaloshin and Ke Zhang present the first complete proof of Arnold diffusion. Their proof demonstrates that typical perturbations of five-dimensional integrable systems, characterized by two and a half degrees of freedom, exhibit topological instability. This achievement fulfills a plan announced by John Mather in 2003 but remained unfinished until his passing. Kaloshin and Zhang adopt Mather's strategy while emphasizing a more Hamiltonian approach, integrating normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Their book provides a comprehensive, clear, and modern explanation of the proof's steps, accompanied by a thorough account of background material. With its accessibility to students and researchers alike, this book constitutes a critical contribution to mathematical physics and dynamical systems, particularly Hamiltonian systems.

\n Weight: 348g\n
Dimension: 156 x 234 x 16 (mm)\n
ISBN-13: 9780691202525\n \n