Albert Meads Fisher
Department of Mathematics, University of São Paulo
Institute of Mathematics and Statistics
University of São Paulo
Google Scholar Citations
USP Digital
Areas of Interest

Dynamical Systems

Ergodic Theory

Probability Theory

Complex dynamics
This shows the fundamental solution of
onedimensional heat equation. Black curve marks constant variance.
Click for rotatable 3d image!!
Some papers
Asymptotic selfsimilarity and ordertwo ergodic theorems for
renewal flows,
Journal d'Analyse Mathématique, September 2015, Volume 127, Issue
1, pp 145
(with Marina Talet)pdf,
Distribution of approximants and geodesic flows,
Ergodic Theory and Dynamical Systems, Volume 34,
Issue 06, December 2014, pp 18321848
doi:10.1017/etds.2013.23.
(with Tom Schmidt) pdf,
Dynamical attraction to stable processes,
Ann. Inst. H. Poincaré Probab. Statist. Volume 48, Number 2, 2012,
pp 551578 (with Marina Talet)
pdf,
The selfsimilar dynamics of renewal processes,
Electron. J. Probab. 16, Article 31, May 10, 2011, pp 929961 (with Marina Talet)
pdf,
Minimality and unique
ergodicity for adic transformations,
Journal d'Analyse Mathematique,
109(1): October 2009, pp 131 (with Sebastien Ferenczi and Marina Talet)
pdf,
Nonstationary mixing and the unique ergodicity of
adic transformations, Stochastics and Dynamics, Volume 9 (3), 2009,
pp 335391
pdf,
Anosov families, renormalization and nonstationary subshifts,
Ergodic Theory and Dynamical Systems { 25}, 2005, pp. 661709 (with Pierre Arnoux)
pdf,
(preprint version containing all final corrections for
ETDS; initial preprint Univ. de Marseilles, February 2003),
Smallscale structure via flows,
Expository article: Conference Proceedings,
Fractal Geometry and Stochastics III, Friedrichroda, Germany,
March 1722, 2003, pp 5978
pdf, preprint version:
pdf,
The scenery flow for hyperbolic Julia sets, Proceedings
London Math. Soc. (3) 85, 2002, pp 467492 (with Tim Bedford and Mariusz Urbanski)
pdf,
Exact bounds for the polynomial decay of
correlation, 1/f noise and the {CLT} for the
equilibrium state of a nonHolder
potential,
Nonlinearity, 2001, vol 14, pp 10711104 (with Artur Lopes)
pdf,
The scenery flow for geometric
structures on the torus: The linear setting,
Chinese Annals of
Mathematics
22b, no. 4, 2000, pp 427470 (with Pierre Arnoux)
pdf; (figures are better here than in published version) ,
On invariant line fields,
Bulletin London Math. Soc. 32, 2000, pp 555570 (with Mariusz Urbanski)
pdf
,
A Poisson formula for harmonic projections,
Annales de l'Institut H. Poincaré,
Probabilités et Statistiques
2 (34) 1998,
pp 209216 (with V. Kaimanovich),
pdf
,
Ratio geometry, rigidity and the scenery process for hyperbolic Cantor
sets,
Erg. Th. and Dyn. Sys.
17, 1997,
pp 531564 (with Tim Bedford),
pdf,
Analogues of the Lebesgue density theorem for
fractal sets of reals and integers,
Proc. London Math. Soc. 64,
1992, pp 95124,
pdf,
Second order ergodic theorems for ergodic
transformations of infinite measure spaces,
Proc. AMS
114 (1), 1992,
pp 115128 (with J. Aaronson and M. Denker),
pdf,
Integer Cantor sets and an ordertwo ergodic
theorem,
Ergod. Th. and Dynam. Sys. 13,
1992, pp 4564,
pdf,
Convexinvariant means and a pathwise central limit
theorem,
Adv. Math.
63, 1987,
pp 213246.
pdf.
Expository notes
Smallscale structure and randomness: the scenery flow in
dynamics, geometry and probability (text updated December 2005, references updated March 2009). 34 pp.
pdf,
(English version of thesis for
livredocência,
July 2003, USP;
this is similar to the French or German Habilitation).
Survey of research. 10 pp.
gzipped ps,
(introduction to
research and to the updated version of
the livredocência thesis, December 2005).
Links to some videotaped lectures:
(1.) CUNY Einstein Chair Mathematics Seminar Video, September 22, 1992

Ratio Geometry, Rigidity and the Scenery Process for Hyperbolic Cantor Sets
Abstract of related paper (pdf);
link
to video
(2.) CUNY Einstein Chair Mathematics Seminar Video, September 27, 1994
https://www.math.stonybrook.edu/Videos/Einstein/40819940927Fisher.html

Anosov families, scenery and the Teichmüller flow
Abstract of related paper (pdf);
link to video
(3.) Workshop on Combinatorics, Number Theory and Dynamical Systems,
IMPA, August 1923, 2013

A proof of Moeckel's theorem on continued fractions
Abstract (pdf);
link
to video ;
DOWNLOAD
(4.) Ergodic Optimization and Related Fields, IMEUniversity of Sao Paulo
December 12, 2013: http://iptv.usp.br/portal/video.action?idItem=21407,

Finite and infinite invariant measures for adic transformations
Abstract (pdf);
link
to video; Ergodic Optimization and Related Fields (12/12/2013parte
1), from
1:21:40 to 2:03:45;
to download: link to Download
Helper Firefox addon
(5.) 2nd Workshop on Combinatorics, Number Theory and Dynamical
Systems, IMPA, 2428 August 2015

Fractallike integer sets coming from dynamics
Abstract (pdf);
link to video
Some useful math links
AMS page
MathSciNet
Math links: institutions
Institute of Mathematics and Statistics, University of
São Paulo
IMS, Stony Brook University
Dynamics page, IMS, Stony Brook University
IML, Luminy, Marseilles
CIRM, Luminy, Marseilles
IHES, Paris
IMPA, Rio de Janeiro
MSRI, Berkeley
ESI (Erwin Schrödinger Institute), Vienna
The realworld (!) nonstationary flows depicted here
come from the spectacular site
nullschool.net Earth Wind
Map,
(click on "earth" there for an explanation).
The gif near the top shows surface winds on August
31, 2016. Others show two hurricanes nearing Hawaii, and the jet stream (North Pole
view), same date, and twin hurricanes approaching Florida, Oct. 6.
The interface is GoogleEarth like and the information is almost
realtime, being updated
every three hours. One can view wind speeds at different altitudes, also
currents and wave motion, also concentration of pollutants and ocean surface
temperature anomalies.
And if you are lucky you might see a realworld Reeb Foliation ! Here is
one from June 03, 2017.
Ensinamento, 2a semestre de 2020:
MAT
3211, Algebra Linear