UH Summer school in dynamics: Project
dynamics and beyond
Michael Shub. Endomorphisms
of compact differentiable manifolds
J. Math. 91 1969 175-199.
structural stability of expanding maps on
manifolds. Also some generic theory is
Anthony Manning. There
are no new Anosov diffeomorphisms on tori
Amer. J. Math. 96 (1974)
Shows that the
matrix associated to an Anosov
diffeomorphism of the torus is a hyperbolic
Livsic theorem for matrix cocycles
of Math. (2) 173 (2011), no. 2, 1025-1042.
The title says
Albert Fathi. Expansiveness,
and Hausdorff dimension
. Comm. Math. Phys.
126 (1989), no. 2, 249-262
Hausdorff dimension for expansive systems
and hence for topological dimensions and
other nice things.
Decay of correlations in dynamical systems
Carlangelo Liverani, Central
theorem for deterministic systems (1995)
Matt Nicol's probability lecture on Friday
afternoon derived the CLT using martingale
approximations: this paper gives more
details of this approach.
Dong Han Kim, The
Borel-Cantelli lemma for interval maps
Borel-Cantelli lemma is another result from
probability theory that can sometimes be
proved in a dynamical setting; given a
sequence of events, it addresses the
question of whether finitely many or
infinitely many of them occur.
correlations in piecewise expanding maps,
Journal of Statistical Physics 78 (1995),
This carries out the details of the proof of
decay of correlations using the method of
cones and the Hilbert metric, which will be
discussed in the lectures by Will Ott.
Carlangelo; Saussol, Benoit; Vaienti, Sandro.
probabilistic approach to intermittency.
Ergodic Theory Dynam. Systems 19 (1999), no.
Manneville-Pomeau map was mentioned as an
example of a non-uniformly hyperbolic
dynamical system, which displays
"intermittent" chaotic behaviour; this is
studied in this paper.
Multiplicative ergodic theory and applications
Sebastian Gouezel and Anders Karlsson: Subadditive
and multiplicative ergodic theorems
Mark Pollicott: Maximal
Lyapunov exponents for random matrix
products. Invent. Math. 181 (2010)
of Lyapunov exponents for products of
matrices with positive entries, using
Lai-Sang Young, Ergodic
of differentiable dynamical systems.
and complex dynamical systems (Hillerod, 1993),
293-336, NATO Adv. Sci. Inst. Ser. C Math. Phys.
Sci., 464, Kluwer Acad. Publ., Dordrecht, 1995.
A nice survey
Jairo Bochi: Notes
on a theorem of Furstenberg giving a criterion
for positive exponents
Poincare sections for diagonal maps
A. Wright, From
Billiards to Moduli Spaces, Bull. Amer.
Math. Soc. (2016)
Survey article that gives a description of
the broader context for the lectures. If you
want further (much more detailed) reading,
consider: H. Masur and S.
Tabachnikov, Rational billiards and
Flat surfaces, Handbook of dynamical
systems, Vol. 1A, North-Holland, Amsterdam,
2002, pp. 1015-1089. Also A.
surfaces, Frontiers in number theory,
physics and geometry. I, Springer, Berlin,
2006, pp. 437-583.
Y. Cheung, Hausdorff
of the set of points on divergent trajectories
of a homogeneous flow on a product space
Erg. Th. Dyn. Sys., 27 (2007), 65--85.
dimension itself is not discussed in the
lectures, but you can read this paper with
the goal of understanding the underlying
combinatorial models: continued fractions
and best approximations.
J. Athreya and Y.
Poincare section for the horocycle flow on
the space of lattices, Int. Math. Res.
Not., 2014 no. 10 (2014), 2643-2690.
J. S. Athreya, J.
Chaika, and S. Lelievre. The
gap distribution of slopes on the golden L.
In Recent trends in ergodic theory and
dynamical systems, volume 631 of Contemp.
Math., pages 47-62. Amer. Math. Soc.,
Providence, RI, 2015.