| Summary: | Let <i>H</i> be a compact metric space. The metric of <i>H</i> is denoted by <i>d</i>. And let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>H</mi><mo>,</mo><msub><mi>f</mi><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo>)</mo></mrow></semantics></math></inline-formula> be a non-autonomous discrete system where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>f</mi><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo>=</mo><msubsup><mrow><mo>{</mo><msub><mi>f</mi><mi>n</mi></msub><mo>}</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mo>∞</mo></msubsup></mrow></semantics></math></inline-formula> is a mapping sequence. This paper discusses infinite sensitivity, <i>m</i>-sensitivity, and <i>m</i>-cofinitely sensitivity of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>f</mi><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub></semantics></math></inline-formula>. It is proved that, if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>f</mi><mi>n</mi></msub><mrow><mo>(</mo><mi>n</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> are feebly open and uniformly converge to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>:</mo><mi>H</mi><mo>→</mo><mi>H</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>f</mi><mi>i</mi></msub><mo>∘</mo><mi>f</mi><mo>=</mo><mi>f</mi><mo>∘</mo><msub><mi>f</mi><mi>i</mi></msub></mrow></semantics></math></inline-formula> for any <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>}</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mo>∞</mo></msubsup><mi>D</mi><mrow><mo>(</mo><msub><mi>f</mi><mi>i</mi></msub><mo>,</mo><mi>f</mi><mo>)</mo></mrow><mo><</mo><mo>∞</mo></mrow></semantics></math></inline-formula>, then <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>H</mi><mo>,</mo><mi>f</mi><mo>)</mo></mrow></semantics></math></inline-formula> has the above sensitive property if and only if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>H</mi><mo>,</mo><msub><mi>f</mi><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo>)</mo></mrow></semantics></math></inline-formula> has the same property where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mo>(</mo><mo>·</mo><mo>,</mo><mo>·</mo><mo>)</mo></mrow></semantics></math></inline-formula> is the supremum metric.
|
|---|