Lyapunov Graphs and Flows on Surfaces

1993 ◽  
Vol 340 (2) ◽  
pp. 767 ◽  
Author(s):  
K. A. De Rezende ◽  
R. D. Franzosa
Keyword(s):  
Flows On Surfaces

Combinatorial p-th Ricci flows on surfaces

2021 ◽  
Vol 211 ◽  
pp. 112417
Author(s):  
Aijin Lin ◽  
Xiaoxiao Zhang
Keyword(s):  
Ricci Flows ◽  
Flows On Surfaces

Expansive geodesic flows on surfaces

1993 ◽  
Vol 13 (1) ◽  
pp. 153-165 ◽  
Author(s):  
Miguel Paternain
Keyword(s):  
Geodesic Flow ◽  
Compact Surface ◽  
Conjugate Points ◽  
Riemannian Surface ◽  
Geodesic Flows ◽  
Flows On Surfaces

AbstractWe prove the following result: if M is a compact Riemannian surface whose geodesic flow is expansive, then M has no conjugate points. This result and the techniques of E. Ghys imply that all expansive geodesic flows of a compact surface are topologically equivalent.

Classification of the Morse – Smale flows on surfaces with a finite moduli of stability number in sense of topological conjugacy

2021 ◽  
Vol 29 (6) ◽  
pp. 835-850
Author(s):  
Vladislav Kruglov ◽  
◽  
Olga Pochinka ◽  
◽  
Keyword(s):  
Finite Number ◽  
Limit Cycle ◽  
Topological Classification ◽  
Topological Conjugacy ◽  
Smooth Flow ◽  
Direction Of Movement ◽  
Smale Flows ◽  
Phase Surface ◽  
Flows On Surfaces

Purpose. The purpose of this study is to consider the class of Morse – Smale flows on surfaces, to characterize its subclass consisting of flows with a finite number of moduli of stability, and to obtain a topological classification of such flows up to topological conjugacy, that is, to find an invariant that shows that there exists a homeomorphism that transfers the trajectories of one flow to the trajectories of another while preserving the direction of movement and the time of movement along the trajectories; for the obtained invariant, to construct a polynomial algorithm for recognizing its isomorphism and to construct the realisation of the invariant by a standard flow on the surface. Methods. Methods for finding moduli of topological conjugacy go back to the classical works of J. Palis, W. di Melo and use smooth flow lianerization in a neighborhood of equilibrium states and limit cycles. For the classification of flows, the traditional methods of dividing the phase surface into regions with the same behavior of trajectories are used, which are a modification of the methods of A. A. Andronov, E. A. Leontovich, and A. G. Mayer. Results. It is shown that a Morse – Smale flow on a surface has a finite number of moduli if and only if it does not have a trajectory going from one limit cycle to another. For a subclass of Morse – Smale flows with a finite number of moduli, a classification is done up to topological conjugacy by means of an equipped graph. Conclusion. The criterion for the finiteness of the number of moduli of Morse – Smale flows on surfaces is obtained. A topological invariant is constructed that describes the topological conjugacy class of a Morse – Smale flow on a surface with a finite number of modules, that is, without trajectories going from one limit cycle to another.

scholarly journals Slow entropy for some smooth flows on surfaces

2018 ◽  
Vol 226 (2) ◽  
pp. 535-577
Author(s):  
Adam Kanigowski
Keyword(s):  
Flows On Surfaces

scholarly journals Combinatorial Ricci Flows on Surfaces

2003 ◽  
Vol 63 (1) ◽  
pp. 97-129 ◽  
Author(s):  
Bennett Chow ◽  
Feng Luo
Keyword(s):  
Ricci Flows ◽  
Flows On Surfaces

scholarly journals Ergodicity and topological entropy of geodesic flows on surfaces

2015 ◽  
Vol 9 (01) ◽  
pp. 147-167 ◽  
Author(s):  
Jan Philipp Schröder ◽  
Keyword(s):  
Topological Entropy ◽  
Geodesic Flows ◽  
Flows On Surfaces

Closed cross-sections of irrational flows on surfaces

2006 ◽  
Vol 197 (2) ◽  
pp. 173-192
Author(s):  
S Kh Aranson ◽  
I A Gorelikova ◽  
E V Zhuzhoma
Keyword(s):  
Cross Sections ◽  
Flows On Surfaces
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