scholarly journals Extended Hamilton–Jacobi theory, contact manifolds, and integrability by quadratures

2020 ◽  
Vol 61 (1) ◽  
pp. 012901 ◽  
Author(s):  
Sergio Grillo ◽  
Edith Padrón
Keyword(s):  
Contact Manifolds ◽  
Integrability By Quadratures

scholarly journals Prolongation on contact manifolds

2011 ◽  
Vol 60 (5) ◽  
pp. 1425-1486 ◽  
Author(s):  
Michael Eastwood ◽  
A. Rod Gover
Keyword(s):  
Contact Manifolds

On the non-regularity of tangent sphere bundles

1978 ◽  
Vol 82 (1-2) ◽  
pp. 13-17 ◽  
Author(s):  
David E. Blair
Keyword(s):  
Riemannian Manifold ◽  
Large Class ◽  
Constant Curvature ◽  
Positive Constant ◽  
Contact Structure ◽  
Compact Riemannian Manifold ◽  
Contact Structures ◽  
Sphere Bundle ◽  
Contact Manifolds ◽  
Tangent Sphere

SynopsisClassically the tangent sphere bundles have formed a large class of contact manifolds; their contact structures are not in general regular, however. Specifically we prove that the natural contact structure on the tangent sphere bundle of a compact Riemannian manifold of non-positive constant curvature is not regular.

scholarly journals Geometry of Lie integrability by quadratures

2015 ◽  
Vol 48 (21) ◽  
pp. 215206 ◽  
Author(s):  
J F Cariñena ◽  
F Falceto ◽  
J Grabowski ◽  
M F Rañada
Keyword(s):  
Integrability By Quadratures

scholarly journals Cartan structures on contact manifolds

1981 ◽  
Vol 266 (2) ◽  
pp. 583-583 ◽  
Author(s):  
G. Burdet ◽  
M. Perrin
Keyword(s):  
Contact Manifolds

scholarly journals Legendrian contact homology and topological entropy

2019 ◽  
Vol 11 (01) ◽  
pp. 53-108 ◽  
Author(s):  
Marcelo R. R. Alves
Keyword(s):  
Growth Rate ◽  
Topological Entropy ◽  
Infinite Family ◽  
Contact Structures ◽  
Legendrian Knots ◽  
Contact Homology ◽  
Contact Manifolds ◽  
3 Dimensional ◽  
Reeb Flows ◽  
Legendrian Contact Homology

In this paper we study the growth rate of a version of Legendrian contact homology, which we call strip Legendrian contact homology, in 3-dimensional contact manifolds and its relation to the topological entropy of Reeb flows. We show that: if for a pair of Legendrian knots in a contact 3-manifold [Formula: see text] the strip Legendrian contact homology is defined and has exponential homotopical growth with respect to the action, then every Reeb flow on [Formula: see text] has positive topological entropy. This has the following dynamical consequence: for all Reeb flows (even degenerate ones) on [Formula: see text] the number of hyperbolic periodic orbits grows exponentially with respect to the period. We show that for an infinite family of 3-manifolds, infinitely many different contact structures exist that possess a pair of Legendrian knots for which the strip Legendrian contact homology has exponential growth rate.

scholarly journals Hypersurfaces in almost contact manifolds

1969 ◽  
Vol 21 (3) ◽  
pp. 354-362 ◽  
Author(s):  
D. E. Blair ◽  
G. D. Ludden
Keyword(s):  
Contact Manifolds

scholarly journals $\lambda$ -Symmetries and integrability by quadratures

2017 ◽  
Vol 82 (5) ◽  
pp. 1061-1087 ◽  
Author(s):  
C. Muriel ◽  
J. L. Romero ◽  
A. Ruiz
Keyword(s):  
Integrability By Quadratures
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