Topological Transitivity on the Torus

1994 ◽  
Vol 37 (4) ◽  
pp. 549-551 ◽  
Author(s):  
Sol Schwartzman
Keyword(s):  
Vector Field ◽  
Finite Number ◽  
Fixed Points ◽  
Analytic Vector ◽  
Topological Transitivity ◽  
Topologically Transitive ◽  
Transitive Flow ◽  
Real Analytic ◽  
Analytic Vector Field

AbstractT. Ding has shown that a topologically transitive flow on the torus given by a real analytic vector field is orbitally equivalent to a Kronecker flow on the torus, modified so as to have a finite number of fixed points, provided the original flow had only a finite number of fixed points. In this paper it is shown that the assumption that there are only finitely many fixed points is unnecessary.

scholarly journals Infinitesimal Hartman-Grobman Theorem in Dimension Three

2015 ◽  
Vol 87 (3) ◽  
pp. 1499-1503
Author(s):  
CLEMENTA ALONSO-GONZÁLEZ
Keyword(s):  
Vector Field ◽  
Singular Point ◽  
Principal Part ◽  
Analytic Vector ◽  
Newton Polyhedra ◽  
Real Analytic ◽  
Main Ideas ◽  
Analytic Vector Field

ABSTRACTIn this paper we give the main ideas to show that a real analytic vector field in R3 with a singular point at the origin is locally topologically equivalent to its principal part defined through Newton polyhedra under non-degeneracy conditions.

scholarly journals On a Hsu-Unified Structure Manifold with a Quarter-Symmetric Non-Metric Connection

2013 ◽  
Vol 3 ◽  
pp. 63-70
Author(s):  
Ram Nivas ◽  
Anurag Agnihotri
Keyword(s):  
Vector Field ◽  
Kähler Manifold ◽  
Analytic Vector ◽  
Kahler Manifold ◽  
Metric Connection ◽  
Analytic Vector Field

In the present paper, we have defined a Hsu-unified structure manifold and a Hsu-Kahler manifold and studied some properties of the quarter-symmetric non-metric connection. Certain interesting results on such manifolds have been obtained. We have also studied the properties of the contravariant almost analytic vector field on these manifolds equipped with the quarter-symmetric non-metric connection.

scholarly journals Cyclicity of period annuli and principalization of Bautin ideals

2008 ◽  
Vol 28 (5) ◽  
pp. 1497-1507 ◽  
Author(s):  
LUBOMIR GAVRILOV
Keyword(s):  
Vector Field ◽  
Limit Cycles ◽  
Analytic Vector ◽  
Period Annulus ◽  
Analytic Vector Field

AbstractLet Π be an open period annulus of a plane analytic vector field X0. We prove that the maximal number of limit cycles which bifurcate from Π under a given multi-parameter analytic deformation Xλ of X0 is the same as in an appropriate one-parameter analytic deformation Xλ(ε), provided that this cyclicity is finite. Along the same lines, we also give a bound for the cyclicity of homoclinic saddle loops.

A KAHLER MANIFOLD ADMITTING SEMI-SYMMETRIC METRIC CONNECTION A.

2021 ◽  
Vol 10 (4) ◽  
pp. 2213-2221
Author(s):  
K. Srivastava ◽  
M. M. Kankarej ◽  
S. K. Srivastava
Keyword(s):  
Vector Field ◽  
Kähler Manifold ◽  
Analytic Vector ◽  
Nijenhuis Tensor ◽  
Kahler Manifold ◽  
Metric Connection ◽  
Analytic Vector Field

In present paper we study the properties of Kahler manifold satisfying the semi - symmetric metric connection. Symmetric and skew-symmetric conditions for Nijenhuis tensor of the connection in Kahler manifold has been discussed. The paper also includes some properties of contravariant almost analytic vector field in a Kahler manifold.

A Note on Involutions with a Finite Number of Fixed Points

1968 ◽  
Vol 20 ◽  
pp. 1522-1530
Author(s):  
John D. Miller
Keyword(s):  
Finite Number ◽  
Fixed Points ◽  
Connected Manifold ◽  
Simply Connected

LetMbe a smooth, closed, simply connected manifold of dimension greater than 5. LetTbe an involution onMwith a positive, finite number of fixed points. Our aim in this paper is to prove the following theorem (which is somewhat like that of Wasserman (7)).

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