Lojasiewicz gradient inequality.

Lojasiewicz:

 
\bibitem{Loj}\L{}ojasiewicz, S., {Sur les trajectoires du  gradient d'une fonction analytique}, Seminari di Geometria  1982-1983,  Universit\`a  di Bologna, (1984), 115--117.

Colding and Minicozzi:

 \bibitem{ColdingMinicozzi}Colding, T.H. and Minicozzi, W.P., {\em \L{}ojasiewicz inequalities and applications},  Surveys in Differential Geometry, \textbf{19}\,1, (2014).

Draft paper w Rick Moeckel. 


*************

Yves Colin de Verdiere

Periodic geodesics for contact sub-Riemannian 3D manifolds

arXiv:2202.13743

Theorems: existence of closed sR geodesics.
Start w a closed Reeb orbit. Use that orbits concentrate on it.
in spectral asymptotics



Spectral asymptotics for sub-Riemannian Laplacians
Yves Colin de Verdìère (IF), Luc Hillairet (IDP), Emmanuel Trélat (LJLL (UMR\_7598), CaGE )

https://arxiv.org/abs/2212.02920

*******************

Richard Schwartz.

General mathematical culture.  Control Theory and geometry.

Conway's Nightmare: Brahmagupta and Butterflies
https://arxiv.org/abs/2201.07743

page five, first par. of 


****************

dynamics on manifolds with corners

Kottke.

Uhlmann and Vasy.

Dominic Joyce: analysis on manifold with corners: 

https://arxiv.org/pdf/1605.05913.pdf



 
*********

the Paternains.  

on the relation between
having a Hill boundary and Anosov-ness.

 
Theorem:  if the Hill region for a simple mechanical system on Euclidean
space  is compact
(or more generally: ?   has non-empty boundary)
then the   flow at that energy level is NOT Anosov


the original reference is:

Paternain, Gabriel P.; Paternain, Miguel On Anosov energy levels of
convex Hamiltonian systems. Math. Z. 217 (1994), no. 3, 367–376.

But there is a perhaps slicker proof using the asymptotic Maslov index in:

 Contreras, Gonzalo; Gambaudo, Jean-Marc; Iturriaga, Renato;
Paternain, Gabriel P. The asymptotic Maslov index and its
applications. Ergodic Theory Dynam. Systems 23 (2003), no. 5,
1415–1443.


****************

Laughlin Recommendations

Balancing Stick: 

https://ui.adsabs.harvard.edu/abs/2002PhRvL..89o8702C/abstract

area.  control theory. bio-mechanics.  differential delay eqns.
 

And then here’s the article that points to a possible connection 
of balancing sticks to market processes:

https://ui.adsabs.harvard.edu/abs/2005Chaos..15b6104B/abstract


and a hidden connection to the extra-solar system GSL867:

https://iopscience.iop.org/article/10.3847/1538-3881/aaa894/pdf

Greg has suggested a (do-able!) experiment with a cell phone and a yardstick
based on the balancing stick paper.  

He has notices surprising similarities
(equalities?) of the PDFS - the time series, viewed statistically --  which arise in these three dynamical
systems . 

 general control theory background:

https://arxiv.org/pdf/1605.05913.pdf


****************
 

``Newton's laws and coin-tossing.'' =  Ornstein. Notices of the  AMS.

[in a Dropbox folder : A_Maybe_Read] 

investigation of Bernoulli processes; description of entropy.

In the same general area is this tutorial

Climenhaga and Katok: 

``MEASURE THEORY THROUGH DYNAMICAL EYES'' (2012)

https://arxiv.org/pdf/1208.4550.pdf


    

****************
****************



MISC:  


Hatton-Chen -- curv and area type stuff:

MR3871451 Reviewed
Grong, Erlend (F-PARIS11-SG); Pansu, Pierre (F-PARIS11-M)
Asymptotic expansion of holonomy. (English summary)
Forum Math. 30 (2018), no. 6, 1363–1385.
53C29 (41A60 53C17)

math review of: 

https://mathscinet.ams.org/mathscinet/search/publdoc.html?loc=refcit&refcit=106258&sort=Newest&vfpref=html&r=17&mx-pid=3871451



*****

 

quantum control survey: 

https://arxiv.org/pdf/0910.2350.pdf


********

from River flow to flow maps [ soc science; geography ?]

https://arxiv.org/pdf/2110.09395.pdf


 

B Birnir

Turbulent Rivers [JSTOR]

https://www.jstor.org/stable/43621157

and many papers since ..

*********

https://arxiv.org/pdf/2212.08210.pdf

Kerr space time completely integrability of geod flow

Morava, J  ***



*************

MR3431187 Reviewed
Novelia, Alyssa (1-CA-ME); O'Reilly, Oliver M. (1-CA-ME)
On geodesics of the rotation group SO(3). (English summary)
Regul. Chaotic Dyn. 20 (2015), no. 6, 729–738.
70E40 (53D25)