A CONSTRUCTIVE PROOF OF THE EXISTENCE OF THE PERIODIC SOLUTION OF THE PERIODICITY PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS VIA A NON-INTERIOR POINT ENTROPY CONTINUATION METHOD

2020 ◽  
Vol 22 (2) ◽  
pp. 97-108
Author(s):  
Menglong Su
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Interior Point ◽  
Continuation Method ◽  
Constructive Proof

Smoothness of Asymptotic Phase Revisited

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Flaviano Battelli ◽  
Kenneth J. Palmer
Keyword(s):  
Periodic Solution ◽  
Vector Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stable Manifold ◽  
Autonomous System ◽  
Asymptotic Phase

AbstractIt is well-known that solutions on the stable manifold of a hyperbolic periodic solution of an autonomous system of ordinary differential equations have an asymptotic phase which has the same order of smoothness as the vector field. In this paper we show if the system depends on a parameter that, in general, the asymptotic phase loses one order of smoothness in the parameter.

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