No Constant Solution => No periodic solution

Context: Graduate
Thread starter cacosomoza
Start date Oct 3, 2010
Tags

Constant Periodic

Join the discussion

Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.

Real named experts · corrections over time · the nuance an AI answer skips

1 reply · 2K views

cacosomoza

Thread starter
Oct 3, 2010

Shall f be continuous function of two real variables. Proof that if equation x''=f(x,x') has not constant solutions, then neither it has periodic solutions.

Physics news on Phys.org

Quantum internet leaves the lab with first real-world entanglement over busy telecom fiber
Water-surface vortices drive tiny rotors without electricity, magnets or chemicals
Plasma design rules show how to preserve attosecond flashes for observing electrons

Eynstone

Oct 4, 2010

This follows fom the Poincare-Bendixon theorem : a closed orbit must enclose a stationary point.

No Constant Solution => No periodic solution

Undergrad Why ##a^0=1##?

Undergrad Finding the minimum distance between two curves

Undergrad Mixed approximation vs. full approximation for a power series expansion

Undergrad Correct Upper/Lower limits for continuation of solutions for ODE

High School Arc Length for Hyperbolic Sin

Undergrad Correct Upper/Lower limits for continuation of solutions for ODE

Graduate About ellipticity and a proof that a system of PDEs is elliptic

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

No Constant Solution => No periodic solution

Similar threads