V.I. Arnold's conjecture on avoidance of intersection, Hausdorff codimension, and a structure theorem for finite index maps

DOI10.1016/j.jfa.2016.12.030zbMath1385.47024OpenAlexW2569348222MaRDI QIDQ509736

Yong-Cai Geng, Sumit K. Garg

Publication date: 17 February 2017

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2016.12.030

zbMATH Keywords

Sard's theoremArnold's conjectureavoidance of intersection problemHausdorff dimension and codimensionindex of operatorsrange of smooth operatorsSmale's theoremsmooth finite index maps

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Linear symmetric and selfadjoint operators (unbounded) (47B25) Perturbations of nonlinear operators (47H14) Continuous and differentiable maps in nonlinear functional analysis (46T20) Abstract inverse mapping and implicit function theorems involving nonlinear operators (47J07)

Cites Work

• On the number of Mather measures of Lagrangian systems
• Hausdorff Measure of Critical Images on Banach Manifolds
• An Infinite Dimensional Version of Sard's Theorem
• Hausdorff Conullity of Critical Images of Fredholm Maps
• The measure of the critical values of differentiable maps
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