scholarly journals Robustly non-hyperbolic transitive symplectic dynamics

2018 ◽  
Vol 38 (12) ◽  
pp. 5993-6013 ◽  
Author(s):  
Pablo G. Barrientos ◽  
◽  
Artem Raibekas
Keyword(s):  
Symplectic Dynamics

scholarly journals Conformally Symplectic Dynamics and Symmetry of the Lyapunov Spectrum

1998 ◽  
Vol 194 (1) ◽  
pp. 47-60 ◽  
Author(s):  
Maciej P. Wojtkowski ◽  
Carlangelo Liverani
Keyword(s):  
Lyapunov Spectrum ◽  
Symplectic Dynamics

scholarly journals Symplectic dynamics and the 3-sphere

2019 ◽  
Vol 235 (1) ◽  
pp. 245-254
Author(s):  
Marc Kegel ◽  
Jay Schneider ◽  
Kai Zehmisch
Keyword(s):  
Symplectic Dynamics

scholarly journals First steps towards a symplectic dynamics

2012 ◽  
Vol 17 (1) ◽  
pp. 127-178 ◽  
Author(s):  
B. Bramham ◽  
H. Hofer
Keyword(s):  
Symplectic Dynamics

scholarly journals The conjugation method in symplectic dynamics

2018 ◽  
Vol 35 (1) ◽  
pp. 1-22
Author(s):  
Luis Hernández-Corbato ◽  
Francisco Presas
Keyword(s):  
Symplectic Dynamics ◽  
Conjugation Method

On symplectic dynamics

2018 ◽  
Vol 61 ◽  
pp. 170-196
Author(s):  
Stéphane Tchuiaga
Keyword(s):  
Symplectic Dynamics

scholarly journals When are the invariant submanifolds of symplectic dynamics Lagrangian?

2014 ◽  
Vol 34 (5) ◽  
pp. 1811-1827
Author(s):  
Marie-Claude Arnaud ◽  
Keyword(s):  
Invariant Submanifolds ◽  
Symplectic Dynamics

The symplectic structure for renormalization of circle diffeomorphisms with breaks

2021 ◽  
pp. 2150016
Author(s):  
S. Ghazouani ◽  
K. Khanin
Keyword(s):  
Moduli Spaces ◽  
Symplectic Form ◽  
Symplectic Structure ◽  
Mapping Class ◽  
Character Variety ◽  
Parabolic Bundles ◽  
Dimension Formula ◽  
Renormalization Operator ◽  
Symplectic Dynamics ◽  
Circle Diffeomorphisms

The main goal of this paper is to reveal the symplectic structure related to renormalization of circle maps with breaks. We first show that iterated renormalizations of [Formula: see text] circle diffeomorphisms with [Formula: see text] breaks, [Formula: see text], with given size of breaks, converge to an invariant family of piecewise Möbius maps, of dimension [Formula: see text]. We prove that this invariant family identifies with a relative character variety [Formula: see text] where [Formula: see text] is a [Formula: see text]-holed torus, and that the renormalization operator identifies with a sub-action of the mapping class group [Formula: see text]. This action allows us to introduce the symplectic form which is preserved by renormalization. The invariant symplectic form is related to the symplectic form described by Guruprasad et al. [Group systems, groupoids, and moduli spaces of parabolic bundles, Duke Math. J. 89(2) (1997) 377–412], and goes back to the earlier work by Goldman [The symplectic nature of fundamental groups of surfaces, Adv. Math. 54(2) (1984) 200–225]. To the best of our knowledge the connection between renormalization in the nonlinear setting and symplectic dynamics had not been brought to light yet.

Symplectic dynamics on the universal grassmannian

1992 ◽  
Vol 9 (3) ◽  
pp. 235-253 ◽  
Author(s):  
G. Landi ◽  
C. Reina
Keyword(s):  
Symplectic Dynamics
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