Stability of Critical Points with Interval Persistence
نویسندگان
چکیده
منابع مشابه
Stability of Critical Points with Interval Persistence
Scalar functions defined on a topological space Ω are at the core of many ap-plications such as shape matching, visualization and physical simulations. Topo-logical persistence is an approach to characterizing these functions. It measureshow long topological structures in the sub-level sets {x ∈ Ω : f(x) ≤ c} persistas c changes. Recently it was shown that the critical values de...
متن کاملInvariant Measures for Interval Maps with Critical Points and Singularities
We prove that, under a mild summability condition on the growth of the derivative on critical orbits any piecewise monotone interval map possibly containing discontinuities and singularities with infinite derivative (cusp map) admits an ergodic invariant probability measures which is absolutely continuous with respect to Lebesgue measure.
متن کاملStability of higher-dimensional interval decomposable persistence modules
The algebraic stability theorem for pointwise finite dimensional (p.f.d.) R-persistence modules is a central result in the theory of stability for persistence modules. We present a stability theorem for n-dimensional rectangle decomposable p.f.d. persistence modules up to a constant (2n− 1) that is a generalization of the algebraic stability theorem. We give an example to show that the bound ca...
متن کاملShape Classification According to LBP Persistence of Critical Points
This paper introduces a shape descriptor based on a combination of topological image analysis and texture information. Critical points of a shape’s skeleton are determined first. The shape is described according to persistence of the local topology at these critical points over a range of scales. The local topology over scale-space is derived using the local binary pattern texture operator with...
متن کاملMonodromy and Stability for Nilpotent Critical Points
We give a new and short proof of the characterization of monodromic nilpotent critical points.We also calculate the first generalized Lyapunov constants in order to solve the stability problem. We apply the results to several families of planar systems obtaining necessary and sufficient conditions for having a center. Our method also allows us to generate limit cycles from the origin.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2007
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-007-1356-1