On the singularity structure of invariant curves of symplectic mappings

AbstractWe discuss the singularity structure of Kahan discretizations of a class of quadratic vector fields and provide a classification of the parameter values such that the corresponding Kahan map is integrable, in particular, admits an invariant pencil of elliptic curves.

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Analysis of resonant structures of four-dimensional symplectic mappings, using normal forms

Physical Review E ◽

10.1103/physreve.50.r4298 ◽

1994 ◽

Vol 50 (6) ◽

pp. R4298-R4301 ◽

Cited By ~ 18

Author(s):

E. Todesco

Keyword(s):

Normal Forms ◽

Resonant Structures ◽

Symplectic Mappings

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Invariant curves for area-preserving twist maps far from integrable

Journal of Statistical Physics ◽

10.1007/bf01053746 ◽

1991 ◽

Vol 65 (3-4) ◽

pp. 617-643 ◽

Cited By ~ 6

Author(s):

Alessandra Celletti ◽

Luigi Chierchia

Keyword(s):

Invariant Curves ◽

Twist Maps ◽

Area Preserving

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Invariant curves for variable step size integrators

BIT Numerical Mathematics ◽

10.1007/bf01952792 ◽

1991 ◽

Vol 31 (1) ◽

pp. 169-180 ◽

Cited By ~ 10

Author(s):

Daniel Stoffer ◽

Kaspar Nipp

Keyword(s):

Variable Step Size ◽

Invariant Curves ◽

Step Size ◽

Variable Step

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EXISTENCE OF INVARIANT CURVES FOR MAPS CLOSE TO DEGENERATE MAPS, AND A SOLUTION OF THE FERMI-ULAM PROBLEM

Sbornik Mathematics ◽

10.1070/sm1995v082n01abeh003561 ◽

1995 ◽

Vol 82 (1) ◽

pp. 231-241 ◽

Cited By ~ 9

Author(s):

L D Pustyl'nikov

Keyword(s):

Invariant Curves

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Invariant Curves for Mappings

SIAM Journal on Mathematical Analysis ◽

10.1137/0517075 ◽

1986 ◽

Vol 17 (5) ◽

pp. 1053-1067 ◽

Cited By ~ 38

Author(s):

Hal L. Smith

Keyword(s):

Invariant Curves

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A novel multi-event-based control for robot bilateral tele-operation with an exoskeleton arm under time delay

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes1192 ◽

2009 ◽

Vol 223 (6) ◽

pp. 1481-1491 ◽

Cited By ~ 2

Author(s):

J-F Zhang ◽

C-J Yang ◽

Y Chen

Keyword(s):

Time Delay ◽

Control Structure ◽

Control Architecture ◽

The Internet ◽

Event Generator ◽

Communication Failure ◽

Operation System ◽

Singularity Structure ◽

Control Scheme ◽

Event Based

A novel control architecture based on a multi-event for tele-operation with an exoskeleton arm over the internet in case of transmission delay and communication failure is proposed. In this proposed control scheme a non-time event reference s is chosen to coordinate two sites and promises synchronization of the system. In addition, more than one event generator is employed to compose the multi-event-based control structure, in which the state of the slave site and uncertainties on the master site, such as singularity of the master arm and so on, are both evaluated. Through the bilateral tele-operation experiments in case of time delay with a rigid obstacle and master arm singularity structure, this control scheme is well demonstrated. The tele-operation system has solid performance with good stability and synchronization.

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