@article{1252,
  abstract     = {We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codomain. We provide assumptions under which the homomorphism induced by an outer approximation of a continuous map coincides with the homomorphism induced in homology by the map. In contrast to more classical results we do not require that the projection to the domain have acyclic preimages. Moreover, we show that it is possible to retrieve correct homological information from a correspondence even if some data is missing or perturbed. Finally, we describe an application to combinatorial maps that are either outer approximations of continuous maps or reconstructions of such maps from a finite set of data points.},
  author       = {Harker, Shaun and Kokubu, Hiroshi and Mischaikow, Konstantin and Pilarczyk, Pawel},
  issn         = {1088-6826},
  journal      = {Proceedings of the American Mathematical Society},
  number       = {4},
  pages        = {1787 -- 1801},
  publisher    = {American Mathematical Society},
  title        = {{Inducing a map on homology from a correspondence}},
  doi          = {10.1090/proc/12812},
  volume       = {144},
  year         = {2016},
}

@article{8495,
  abstract     = {In this note, we consider the dynamics associated to a perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and we prove the following result of ``micro-diffusion'': under generic assumptions on $ h$ and $ f$, there exists an orbit of the system for which the drift of its action variables is at least of order $ \sqrt {\varepsilon }$, after a time of order $ \sqrt {\varepsilon }^{-1}$. The assumptions, which are essentially minimal, are that there exists a resonant point for $ h$ and that the corresponding averaged perturbation is non-constant. The conclusions, although very weak when compared to usual instability phenomena, are also essentially optimal within this setting.},
  author       = {Bounemoura, Abed and Kaloshin, Vadim},
  issn         = {0002-9939},
  journal      = {Proceedings of the American Mathematical Society},
  number       = {4},
  pages        = {1553--1560},
  publisher    = {American Mathematical Society},
  title        = {{A note on micro-instability for Hamiltonian systems close to integrable}},
  doi          = {10.1090/proc/12796},
  volume       = {144},
  year         = {2015},
}